Foreign Secretary Dominic Raab has said there are some "positive signs" from the latest data that show the UK is "starting to win this struggle" against coronavirus but warned: "We are still not past the peak."
Speaking at Monday's Downing Street press conference, Mr Raab praised people for staying at home during the Easter weekend and added: "Our plan is working. Please stick with it and we'll get through this crisis together."
Mr Raab said: "At the end of last week we were concerned that people might start ignoring the advice or cutting corners given the temptation to go out into the sunshine.
"In fact the overwhelming majority of people stayed at home and understood the importance of doing so.
"By staying home this weekend, you've saved lives.
"Thank you, your efforts are making all the difference. And please keep them up – we've come too far, we've lost too many loved ones and we've sacrificed too much to ease up now."
Mr Raab's comments came after the hospital death toll passed 11,000 and Downing Street said the Government's Covid-19 testing regime was "heading in the right direction".
Prime Minister Boris Johnson's official spokesman maintained the UK was still on course to carry out the Government's pledge of 100,000 coronavirus tests a day by the end of the month as he said 18,000 had been conducted in the 24 hours to Sunday morning.
The spokesman said there had been "significant progress" in the attempt to improve testing of frontline NHS workers, with nearly 43,000 staff and their families tested so far.
On Monday, Mr Johnson's spokesman said: "So we have more to do, but we are heading in the right direction."
Latest figures from the Department of Health showed 14,506 tests on 10,745 people were carried out on Sunday, excluding data from Northern Ireland.
The Government has come under pressure to increase testing of frontline health workers and, on April 3, Health Secretary Matt Hancock said around 1,500 staff were being tested daily.
On Monday, the PM's spokesman said: "In terms of tests of NHS staff and their families, in the 24 hours up to 9am yesterday, 2,630 tests were carried out by commercial partners, which means those drive-through sites.
"And now, in total 42,812 NHS staff and their families have been tested in total, which marks significant progress on where we were a little over a week ago."
The comments came as the Department of Health said 11,329 people had died in hospitals as of 5pm on Sunday, with many more expected in care homes.
It means the UK has more recorded deaths than any county except the US, Italy, Spain and France.
Mr Johnson's spokesman said the Prime Minister had tested negative for coronavirus on leaving hospital following his admission to an intensive care unit and would follow medical advice on when to return to work.
A review of lockdown measures will take place by Thursday, the deadline set out in law.
Ministers have said they want to be sure the UK is past the peak of the outbreak before easing the restrictions, but 10 members of the Cabinet are reportedly urging lockdown conditions to be eased amid concerns about the impact on the economy.
The Times quoted an unnamed minister as saying it was important not to do "more damage", and measures could be eased after another three weeks.
Scientific advisers will meet on Tuesday ahead of the formal review of the strict social distancing measures on Thursday, the deadline set out in law.
Chancellor Rishi Sunak, who warned during his Budget last month that the UK risks falling into recession as a result of disruption caused by coronavirus, has injected £14 billion from the coronavirus emergency response fund into the NHS and local authorities.
It is hard to find the words to express my debt to the NHS for saving my life.
The efforts of millions of people across this country to stay home are worth it. Together we will overcome this challenge, as we have overcome so many challenges in the past. #StayHomeSaveLivespic.twitter.com/HK7Ch8BMB5
— Boris Johnson #StayHomeSaveLives (@BorisJohnson) April 12, 2020
– Mr Johnson continued his recovery from Covid-19 at Chequers in Buckinghamshire after doctors ordered the Prime Minister to rest.
– Spain, which on Sunday reported its lowest daily growth in infections for three weeks, allowed workers in some non-essential industries to return to factories and construction sites on Monday.
– The latest analysis from Johns Hopkins University in the US suggested the UK's case fatality rate, the number of deaths per 100 confirmed cases, was 12.5%, behind only Italy's rate of 12.7%.
– The Ministry of Defence said nearly 200 members of the armed forces are being loaned to five NHS ambulance trusts to support their work during the pandemic.
– Nearly 3,000 fire and rescue staff are in self-isolation and unable to work, according to the Fire Brigades Union.
The Government continues to face pressure over shortages of personal protective equipment (PPE) for frontline NHS staff, as a growing number of health workers died.
Chris Hopson, chief executive of NHS Providers in England, which represents hospital trusts, told BBC Breakfast the supply of gowns, imported from China, was "hand-to-mouth".
He said the NHS ordered "a whole load of stock" weeks ago, but delays have been caused by the product sometimes failing safety tests, while other batches have been mislabelled, meaning the NHS has ended up with additional masks.
Sue Hill, a vice president of the Royal College of Surgeons, said she believed the death toll could reach 30,000, as she criticised the daily briefings by ministers as a "bit of a joke".
Referring to PPE, she told The Guardian: "The thing that irritates me is Cabinet ministers are standing up every day, addressing us as if we're on a war footing and giving Churchillian quotes when they could be doing a few simple things like getting more bits of plastic and paper on to wards."
At the weekend, the Royal College of Nurses issued new guidance that nurses who could not get adequate PPE should, as a "last resort", refuse to work.
Following his hospital release, Mr Johnson said in an emotional speech posted on social media that it "could have gone either way" for him, and thanked NHS staff for saving his life.