Police are investigating Margaret Ferrier MP for alleged breaches of coronavirus laws after she took a train from London to Scotland knowing she had coronavirus.
SNP leader Nicola Sturgeon said she had made it "crystal clear" in a call with Ms Ferrier, who has had the whip withdrawn by the SNP, she should resign her seat following the "monumental" error of judgment.
The Metropolitan Police said it is "conducting an investigation into potential offences" with British Transport Police.
The London force said in a statement: "An investigation is under way into reported breaches of the Health Protection Regulations 2020.
"On Thursday October 1, a Member of Parliament contacted Police Scotland to report she may have breached legislation and guidance relating to Covid-19.
"This related to her actions earlier this week, including a train journey on Tuesday September 29, between London and Glasgow, following a positive Covid-19 test.
"Following consultation with Police Scotland, officers from the Metropolitan Police, working with British Transport Police, are conducting an investigation into potential offences.
"The Parliamentary Commissioner for Standards has been informed."
Pictures of the week: September 27 - October 3
Pictures of the week: September 27 - October 3
England's Lee Westwood, right, and Ian Poulter bump feet after they finish their rounds on the ninth green during the second round of the Scottish Open at The Renaissance Club, North Berwick, Scotland, Friday, Oct. 2, 2020. (Jane Barlow/PA via AP)
Mark Cummins using a misting and fogging machine to clean and disinfect the Grand Central venue in Liverpool city centre. (Photo by Danny Lawson/PA Images via Getty Images)
Artist Cold War Steve with his new piece of art, Trumpscape, outside the Liver Building in Liverpool, England, Friday Oct. 2, 2020. The 144-piece, 140m² artwork is an apocalyptic vision of Trump's America in the age of coronavirus.(Danny Lawson/PA via AP)
People walk in Piccadilly Circus as heavy rain batters the capital, in London, Friday, Oct. 2, 2020. Britain is facing gales and heavy downpours as the the storm "Alex" in reaching it's coasts. (AP Photo/Alberto Pezzali)
A dog wears a Free Assange balloon as he stands with demonstrators outside the Old Bailey in London, Thursday, Oct. 1, 2020, as the Julian Assange extradition hearing to the US ended, with a result expected later in the year. (AP Photo/Kirsty Wigglesworth)
Arsenal's goalkeeper Bernd Leno makes a save during the English League Cup fourth round soccer match between Liverpool and Arsenal at Anfield, Liverpool, England, Thursday, Oct. 1, 2020. (Peter Byrne/Pool via AP)
UK Prime Minister Boris Johnson and US President Donald Trump are pictured in this panel.
Caricatures of politicians on large advertisement board for satirical television puppet show Spitting Image inside Westminster Tube Station. (Photo by Keith Mayhew / SOPA Images/Sipa USA)
Waves crash along the coast at Swanage in Dorset. Parts of the UK are preparing to be lashed by heavy rain and high winds as Storm Alex heralds the arrival of a stretch of bad weather over the weekend.
NORTH BERWICK, SCOTLAND - OCTOBER 02: Robert MacIntyre of Scotland chips onto the 11th green during the second round of the Aberdeen Standard Investments Scottish Open at The Renaissance Club on October 02, 2020 in North Berwick, Scotland. (Photo by Ross Kinnaird/Getty Images)
A pedestrian is seen carrying a window on London Bridge by The City of London as the second wave of Coronavirus hits London on September 30, 2020, London, England. (Photo by Dominika Zarzycka/NurPhoto via Getty Images)
SOLIHULL, ENGLAND - SEPTEMBER 30: Lucy Graham (R), Rikke Sevecke and Megan Finnigan (L) of Everton during the Vitality Women's FA Cup Semi Final match between Birmingham City and Everton on September 30, 2020 in Solihull, England. Sporting stadiums around the UK remain under strict restrictions due to the Coronavirus Pandemic as Government social distancing laws prohibit fans inside venues resulting in games being played behind closed doors. (Photo by Emma Simpson - Everton FC/Everton FC via Getty Images)
Actors dressed as pantomime dames stop at the entrance of Downing Street as they march on Parliament to demand more support for the theatre sector amid the COVID-19 pandemic in London, Wednesday, Sept. 30, 2020. (AP Photo/Frank Augstein)
Art work by graffiti artist The Rebel Bear which has recently appeared showing two children about to detonate explosives at a cashline at a shopping centre in Cambuslang. Over recent months the artist has drawn several coronavirus related drawings in Glasgow. (Photo by Andrew Milligan/PA Images via Getty Images)
Weapon Systems Officer First Lieutenant Trey Pollard of the United States Air Force's (USAF) 48th Fighter Wing, stationed at RAF Lakenheath in Suffolk, prepares for take off in an F-15E Strike Eagle at RAF Coningsby in Lincolnshire, supported by UK ground crews as part of a training exercise, using what USAF calls Agile Combat Employment (ACE) concepts.
LONDON, UNITED KINGDOM - SEPTEMBER 30: One of four postboxes across the United Kingdom to be painted black to honour black Britons as seen here in Brixton on September 30, 2020 in London, England. Decorated to honour comedian Lenny Henry, nurse Mary Seacole, footballer Walter Tull and artist Yinka Shonibare, the Royal Mail postboxes in London, Glasgow, Cardiff and Belfast have been unveiled to coincide with Black History Month 2020. (Photo by Leon Neal/Getty Images)
GOLD COAST, AUSTRALIA - SEPTEMBER 30: Art installation 'Gaia' is seen on display at HOTA on September 30, 2020 in Gold Coast, Australia. The work by UK artist Luke Jerram measures seven metres in diameter, with internal lighting combining 120dpi detailed NASA imagery of the Earth. The spherical sculpture is accompanied by a specially made surround sound composition by composer Dan Jones. (Photo by Quinn Rooney/Getty Images)
A rainbow at sunrise over the Watch House Museum at Seaton Sluice in Northumberland. (Photo by Owen Humphreys/PA Images via Getty Images)
Workers from the event industry protest at Parliament Square in London, Tuesday, Sept. 29, 2020, demanding help for their industry after the shutdown due to the coronavirus outbreak. (AP Photo/Frank Augstein)
An elderly woman in a protective face mask is seen walking near Oxford Street as cases of Covid-19 continue to rise in fear a second wave of pandemic will take over the city and London will face a new lockdown In London, England, on September 29, 2020.. (Photo by Dominika Zarzycka/NurPhoto via Getty Images)
A group of people gathered on Wardour Street after closing time in Soho, central London, after a range of new restrictions to combat the rise in coronavirus cases came into place in England. (Photo by Yui Mok/PA Images via Getty Images)
Liverpool's Brazilian goalkeeper Alisson Becker reacts after Liverpool's Portuguese striker Diogo Jota (unseen) scored his team's third goal during the English Premier League football match between Liverpool and Arsenal at Anfield in Liverpool, north west England on September 28, 2020. (Photo by JASON CAIRNDUFF / POOL / AFP) / RESTRICTED TO EDITORIAL USE. No use with unauthorized audio, video, data, fixture lists, club/league logos or 'live' services. Online in-match use limited to 120 images. An additional 40 images may be used in extra time. No video emulation. Social media in-match use limited to 120 images. An additional 40 images may be used in extra time. No use in betting publications, games or single club/league/player publications. / (Photo by JASON CAIRNDUFF/POOL/AFP via Getty Images)
STANSTED, ESSEX - SEPTEMBER 28: The INEOS TEAM UK America"u2019s Cup race boat being towed onto an Antonov cargo plane by the teams new prototype INEOS "u2018Grenadier"u2019 4x4 at the start of its journey to Auckland, New Zealand on September 28, 2020 in Stansted, United Kingdom. (Photo by Lloyd Images/Getty Images)
MANCHESTER, ENGLAND - SEPTEMBER 28: Isolating students peer out of their accommodation window as they are interviewed by a television crew on September 28, 2020 in Manchester, England. Around 1,700 students across two student housing blocks were told to self-isolate after more than 100 students recently tested positive for Covid-19. The students were told to self-isolate for 14 days even if they were not experiencing symptoms. (Photo by Christopher Furlong/Getty Images)
NOTE TO EDITORS. FOR USE IN RELATION TO THE EXHIBITION ONLY. A member of staff looks at 'Head II" by Tim Shaw at a preview for the 'summer' exhibition at the Royal Academy of Arts in London. The 252nd Summer Exhibition was postponed because of the coronavirus pandemic and will take place in the autumn for the first time. (Photo by Kirsty O'Connor/PA Images via Getty Images)
Britain's Prime Minister Boris Johnson takes part in a game of cricket in a sports lesson during a visit to Ruislip High School in his constituency of Uxbridge, west London, Monday Sept. 28, 2020. Lawmakers and scientists have criticized Johnson's Conservative government for problems with the national test-and-trace program that was supposed to help control the spread of the disease and reduce the need for limits on social interactions. (Stefan Rouseau/PA via AP)
Chinese contemporary artist and activist Ai Weiwei stands with protesters outside the Old Bailey in support of Julian Assange's bid for freedom during his extradition hearing, in London, Monday, Sept. 28, 2020. (AP Photo/Kirsty Wigglesworth)
Two women look at a selection of the artworks on display, including 'The American Dream' by Grayson Perry RA (C), during a press preview of the 252nd Summer Exhibition at Royal Academy of Arts, on September 28, 2020 in London, England. The exhibition, which for the first time ever, due to COVID-19, takes place in the Autumn between 6 October 2020 and 3 January 2021, features over 1000 works in a range of media, by emerging and established artists. (Photo by WIktor Szymanowicz/NurPhoto via Getty Images)
Winter Thorn in the parade ring prior to Read Silvestre De Sousa Blog At starsportsbet.co.uk Novice Stakes at Nottingham Racecourse.
The Milky Way seen above Derwentwater in the Lake District.
LONDON, ENGLAND - SEPTEMBER 27: Mascots are displayed on the big screen during the Premier League match between Tottenham Hotspur and Newcastle United at Tottenham Hotspur Stadium on September 27, 2020 in London, England. Sporting stadiums around the UK remain under strict restrictions due to the Coronavirus Pandemic as Government social distancing laws prohibit fans inside venues resulting in games being played behind closed doors. (Photo by Tottenham Hotspur FC/Tottenham Hotspur FC via Getty Images)
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Ms Ferrier could face a £4,000 fine for a first-time offence of coming into contact with others when she should have been self-isolating.
Prime Minister Boris Johnson told BBC Scotland it is vital "everyone obeys the rules and the guidance" regarding coronavirus.
He said that, in March and April, people in Scotland and across the UK "came together and got the virus down", but he added: "Alas what happened since then is that everyone got a bit... complacent and a bit blase.
"I think everybody should stick to the rules and that's what they are there for.
"We've seen they did make a huge difference."
Speaking at her daily coronavirus briefing on Friday, Scotland's First Minister said Ms Ferrier should "come to the right decision" and step down as an MP.
Ms Sturgeon said: "This was a monumental, actually almost incomprehensible, error of judgment on Margaret's part, and I can't make my feelings on that any clearer than I am doing.
"There surely can be nobody in this country who doesn't know that if you have a positive test for Covid you should isolate yourself, and you certainly shouldn't sit on a train for six hours taking a 450-mile journey."
Ms Ferrier issued an apology on Thursday evening as she revealed she was tested for coronavirus on Saturday after developing symptoms, but then took a train to Parliament on Monday when she should have been self-isolating.
She spoke in a Commons debate on coronavirus on Monday, and was told at some point that evening she had tested positive.
Instead of self-isolating, she took a train back to Scotland on Tuesday.
SNP staff at Westminster say they were told on Wednesday Ms Ferrier had coronavirus, and initially thought she had taken the test after returning to Scotland, only learning about her breaches of self-isolation rules on Thursday.
Ms Sturgeon said on Friday Ms Ferrier had been unable to give a "cogent explanation" for her actions.
The MP is now facing growing calls to quit, with Ms Sturgeon saying she has herself told her to resign but Ms Ferrier did not reveal what she intends to do.
The First Minister added: "I don't have the power to force an MP to sit down, no party leader has that power.
"But I can make my views known and, difficult though it is, I have done so, and I hope she will come to the right decision."
She added: "This is not a minor breach of the rules, it is not an inadvertent breach of the rules, it is a really flagrant and dangerous breach of the rules."
Her tough stance was echoed by SNP Westminster leader Ian Blackford, who insisted Ms Ferrier's position as an MP is untenable following her "tremendous error of judgment", telling BBC Radio Scotland's Good Morning Scotland programme she will "have to do the right thing".
Commons Speaker Sir Lindsay Hoyle described her actions as "completely reckless behaviour", and said he found out while in the Speaker's Chair at around 4pm on Wednesday.
He told Sky News the reaction was immediate and "within 20 minutes we were in full swing on what we needed to do to ensure the safety and security of staff and members".
The Speaker's Office alerted DUP MP Jim Shannon he was a close contact of a positive case on Wednesday, having been seated at a socially-distanced dining table with Ms Ferrier on Monday evening.
His party's statement said he immediately self-isolated and continues to do so as a precaution, after a negative test result on Thursday.
A number of other SNP MPs, including David Linden whose Glasgow East constituency neighbours Ms Ferrier's, also called for her to quit.
Ms Ferrier, the Rutherglen and Hamilton West MP, said she took a test on Saturday afternoon after experiencing "mild symptoms", meaning she should have self-isolated.
In a statement, she said she travelled home to Cambuslang, South Lanarkshire, on Tuesday, where she has been self-isolating ever since.
She apologised for her actions and said there was "no excuse".
UK Communities Secretary Robert Jenrick told BBC Radio 4's Today programme: "Margaret Ferrier has accepted that she has broken the law.
"That's now a matter for the police, the authorities who are investigating the matter, and it is really for her to consider what her political future is, and for her party, the SNP."
Scottish Conservative leader Douglas Ross said her actions were "reckless and dangerous", and her position as an MP is now "completely untenable".