The prime minister is considering a month-long lockdown across England in the hope that measures could be eased before Christmas, documents suggest.
A new “stay at home” order could be announced on Monday, with schools, colleges and universities exempt.
Documents seen by the BBC suggest the UK is on course for a much higher death toll than during the first wave unless further restrictions are introduced.
Deaths could reach more than 4,000 a day, one of the models suggests.
This figure is based on no policies being brought in to slow the spread of the disease.
At the height of the pandemic during the spring, deaths reached more than 1,000 a day.
The papers seen by the BBC are understood to be part of a presentation by the government’s pandemic modelling group SPI-M shown to Boris Johnson.
All the models in the document predict that hospitalisations are likely to peak in mid-December, with deaths rising until at least late December before falling from early January.
Another document, based on NHS England modelling from 28 October, warns that the NHS would be unable to accept any more patients by Christmas, even if the Nightingale hospitals are used and non-urgent procedures cancelled.
The document warns that south west England and the Midlands will be the first to run out of capacity, potentially within a fortnight.
A government source said that the country is at a “crunch point”.
No final decisions have yet been taken, and not all cabinet members have yet been consulted on the next steps.
But it seems that Mr Johnson is likely to take the national action that he swore he would do everything to avoid.
These latest papers come after official documents from the Scientific Advisory Group for Emergencies (Sage) revealed that Covid is spreading much faster in England than the predicted “worst-case” scenario, which estimated there could be 85,000 deaths from Covid during winter.
The Sage documents, dated 14 October and published on Friday, revealed that scientists estimated that, by mid-October, there were between 43,000 and 74,000 people being infected with coronavirus every day in England.
‘We have to act now’
Suggestions of a national lockdown have been welcomed by government advisers and scientists.
Prof Gabriel Scally, a Sage member, told BBC’s Newsnight that a national lockdown was inevitable.
“The R number is still far too high. Everyone knows that these tiers are not working and they’re not going to work.
“We could have got away with a shorter circuit-breaker if it had been done earlier but now I think the numbers are accelerating so fast that there is nothing left in the armoury anymore except really quite a serious lockdown.”
Prof Devi Sridhar, chair of global and public health at the University of Edinburgh, told BBC Radio 4’s Any Questions there was “no choice” but to introduce a nationwide lockdown in England.
“The later and the longer they delay to go into it, it’s going to last longer.”
And Prof Jeremy Farrar, also a Sage member, wrote on Twitter: “To bring Covid-19 under control, we have to act now.”
He added: “We have quickly breached the reasonable worst-case scenario, we are further ahead in this phase of the epidemic than many have assumed.”
The current estimate of the R number in the UK – the number of people each infected person passes the virus on to on average – is between 1.1 and 1.3, indicating that cases are still growing.
On Friday, 274 deaths were announced, meaning that since the start of the pandemic 46,229 people have died within 28 days of a positive test.
The government’s current strategy is focused on local restrictions to control the virus.
Every area of England is now in one of three coronavirus alert categories – medium (tier one), high (tier two) or very high (tier three). Scotland has five levels of restrictions.
Nottinghamshire has become the latest region to join the top tier of Covid-19 restrictions, after an overall rise in infection rates and West Yorkshire will join the third tier from Monday, at which point nearly a fifth of England will be under the toughest restrictions.
Meanwhile, more than a dozen regions in England will move from the lowest to the middle tier of restrictions on Saturday.
Scotland’s new tiered system of restrictions will come into force at 06:00 on Monday, and Wales remains under a 17-day “firebreak” lockdown until 9 November.
And Wales’ First Minister Mark Drakeford said a new set of national rules will be brought in once the lockdown ends, rather than a “network of local restrictions”.
Pubs and restaurants in Northern Ireland were closed for four weeks starting on 16 October, with the exception of takeaways and deliveries. Schools were closed for two weeks.