Boris Johnson is warning that a second wave of coronavirus has arrived in the UK, as scientists reported the "widespread growth" of the virus across the country.
The Government's Scientific Advisory Group for Emergencies (Sage) said the R number – representing the number of people an infected person will pass the virus to – has risen to between 1.1 and 1.4, meaning cases could rise very quickly.
As ministers announced tough new restrictions affecting 13.5 million people, Mr Johnson said they would "keep everything under review".
"There's no question, as I've said for several weeks now, that we could expect (and) are now seeing a second wave coming in," he told reporters during a visit to the Vaccines Manufacturing Innovation Centre construction site near Oxford.
"We are seeing it in France, in Spain, across Europe – it has been absolutely, I'm afraid, inevitable we were going to see it in this country."
Public Health England (PHE) warned that data published on Friday could be a sign of "far worse things to come", as the Office for National Statistics (ONS) said cases are thought to have almost doubled in a week to 6,000-a-day in England.
Kevin McConway, emeritus professor of applied statistics at the Open University, described the latest R figure as "undoubtedly concerning".
He said: "Even at growth rates within the estimated range, the number of new cases could grow to high levels quickly if the interventions are not sufficiently effective."
It comes as ministers discuss whether further national restrictions are needed, such as forcing pubs and restaurants to close at 10pm or curbs on people socialising.
The Prime Minister insisted that he did not want a second national lockdown, but said it was essential that people followed social distancing guidelines – including the new "rule of six".
"But as we look at this particular curve and what is happening now, clearly we are going to keep everything under review. I don't want to get into a second national lockdown at all, it is the last thing anybody wants," he said.
"I don't want to go into bigger lockdown measures at all, we want to keep schools open and it is fantastic the schools have gone back in the way they have. We want to keep the economy open as far as we possibly can, we want to keep businesses going.
"The only way we can do that is obviously if people follow the guidance."
Ministers are thought to be considering a two-week national "circuit break", an attempt to break the chain of transmission.
Earlier, however, Health and Social Care Secretary Matt Hancock stressed the focus remained on local interventions, as he announced new restrictions for large parts of England's North West, West Yorkshire and the Midlands.
He pointed to a worrying rise in cases, with Merseyside, Warrington, Halton and Lancashire – excluding Blackpool and Greater Manchester – escalated to "areas of intervention".
From Tuesday, the following restrictions will be enforced in these places:
– Residents must not socialise with other people outside of their own households or support bubble in private homes and gardens.
– Restaurants, pubs and bars will be restricted to table service only, while all leisure and entertainment venues including restaurants, pubs and cinemas must close between 10pm and 5am.
— Boris Johnson (@BorisJohnson) September 18, 2020
Residents are also advised to avoid public transport unless it is essential, as well as professional or amateur sporting events.
The new rules do not apply to Bolton or Greater Manchester, where separate restrictions are already in place.
Meanwhile, in the Midlands, people in Oadby and Wigston will be banned from socialising with others outside of their own household or support bubble in private homes and gardens from Tuesday.
In West Yorkshire, people in all parts of Bradford, Kirklees and Calderdale will be subject to the same ban on socialising.
Overall, around 13.5 million people are currently living under restrictions or will be from Tuesday.
On Friday, new confirmed daily cases of coronavirus hit 4,322 – the highest since May 8.
Cases of the virus and hospital admissions for Covid-19 are doubling every seven to eight days in the UK, according to the new data.
All regions of England, except the South West, also have an R that is higher than 1.0, and all have positive growth rates.
Although deaths are currently low, experts expect them to rise, with Sage saying the R number "shows that we are moving to wider spread growth in transmission at a faster rate".
Last week, the R number was said to be between 1.0 and 1.2.
Meanwhile, the ONS said its latest estimate "shows the number of infections has increased in recent weeks".
Overall, an average of 6,000 people in England per day were estimated to be newly infected with Covid-19 between September 4 and 10, almost double the 3,200 people per day from August 30 to September 5.
The figures do not include people staying in hospitals or care homes.
Yvonne Doyle, medical director at Public Health England, said: "We're seeing clear signs this virus is now spreading widely across all age groups and I am particularly worried by the increase in rates of admission to hospital and intensive care among older people.
"This could be a warning of far worse things to come."
The Government is still under fire over the NHS Test and Trace system, which has seen up to four times the number of people trying to book a test as the number of tests available.
Experts have said that without effective testing and tracing, it will be much harder to control the spread of the virus and pinpoint larger outbreaks.
Globally, confirmed cases of the coronavirus have topped 30 million worldwide, according to figures from Johns Hopkins University.