A month-long lockdown across England is being considered by the prime minister in the hope that measures could be eased before Christmas, documents suggest.
A new "stay at home" order, with schools, colleges, and universities exempt, could be announced on Monday.
Documents seen by the BBC suggest that, unless further restrictions are introduced, the UK is on course for a much higher death toll than during the first wave.
Deaths could reach more than 4,000 a day, suggests one of the models.
This figure is based on no policies being introduced to slow the disease's spread.
Deaths reached more than 1,000 a day at the height of the pandemic during the spring.
The papers seen by the BBC are understood to be part of a presentation shown to Boris Johnson by the government's pandemic modeling group SPI-M.
All the models in the document predict that hospitalizations are likely to peak in mid-December, with fatalities rising before falling from early January until at least late December.
Another paper, based on the modeling of NHS England from 28 October, warns that by Christmas the NHS would not be able to accept any more patients, even if Nightingale hospitals were used and non-urgent procedures were canceled.
The document warns that the first to run out of capacity, potentially within a fortnight, will be south-west England and the Midlands.
"The country is at a crunch point," a government source said.
There have been no final decisions yet, and not all members of the Cabinet have been consulted on the next steps.
But Mr. Johnson, it seems, is likely to take national action that he swore he would do everything he could to avoid.