The projections - which operate under a number of assumptions including a worst-case scenario that the Omicron variant of coronavirus is 50% as severe as Delta - also indicate that daily COVID-19 deaths could peak at nearly 3,000 if the country remains under 'Plan B' rules.
The number of daily hospitalisations could reach as high as 15,000 per day.
On 24 December, the UK Health Security Agency estimated that someone with Omicron is between 31% and 45% less likely to attend A&E and 50% to 70% less likely to be admitted to hospital than an individual with the Delta variant.
Current restrictions under Plan B include measures such as work from home guidance, compulsory mask wearing on public transport and in shops, and proof of vaccination or a negative test to attend large events or nightclubs.
The modelling, which is a pre-print and carried out by experts at the University of Warwick, projects whether outcomes would be significantly different if Step 1 restrictions - last seen in March and which included measures like the reopening of schools, and the rule of six in outdoor gatherings, but no indoor gatherings - were re-introduced.
It suggests its introduction by 19 December would have had a significant impact on numbers, but finds its introduction in the next several days will fail to have significant impact on the trajectory.
In the report - which is used by the Scientific Advisory Group for Emergencies (Sage) - experts also warn that rising infections have the potential to "disrupt many services" alongside high hospitalisations which "will place a severe burden on the health services".
The report's authors write: "In the absence of additional controls, with England remaining under Plan B (dark red lines), we project a large wave of infection, leading to hospital admissions peaking at 13,600 per day (9,300-21,3000) and deaths peaking at 2,890 per day (1,800-4,770)."
They add: "Our projections show that Omicron, due to its rapid growth, can generate levels of infection that could disrupt many services and levels of hospital admissions that will place a severe burden on the health services.
"Determining the optimal control policy is highly dependent on the objective, but several general conclusions can be drawn.
"First, strong controls enacted early bring the greatest reduction in infections, hospital admissions and deaths during the first wave of Omicron.
"Second, small initial waves lead to larger exit waves, with exit waves of deaths and hospital admission relatively larger than the exit wave of infection due to changes in the age distribution of infection.
"However, such later exit waves, which tend to peak in April 2022, provide the opportunity to learn more about the Omicron variant and to instigate specific controls."
The scenario is one of a number of outcomes modelled by the scientists.
Commenting on the new data, Professor Christina Pagel from University College London said that another of the scenarios - one in which Omicron was 80% less severe than Delta - was more likely to reflect the current situation.
In such a scenario, the experts project a peak of 1,000 daily COVID deaths, up to 5,000 daily hospital admissions and still around 1.4 million infections each day. (See charts below, which broadly reflect the current Plan B restrictions)
She tweeted: "My take on it. TLDR: things are pretty bad and I'm sad & bewildered at lack of govt action and general levels of hopium."
Adding: "Many from govt to scientists to the media to the public have decided that 100,000s cases a day are fine. We are dangerously weakening our NHS & its staff. Too many people will end up with chronic illness & too many will die. All I can do is keep saying it's not fine."
According to the latest figures, there were 2,082 COVID-19 hospital admissions in England on Wednesday, up 90% week-on-week and the highest number since 3 February. Concerns are growing about the large numbers of NHS and care workers being forced to isolate.
Chris Hopson, the head of NHS Providers, said staff absences were “clearly now having a significant impact” across parts of the health service.
“NHS experience suggests that the impact varies considerably depending on how many staff are isolating, driven by local community infection rates; ability to rapidly source temporary replacement staff; and ability to flex existing staff to cover work of those who are absent,” he said.
Boris Johnson has continued to insist people should proceed with their New Year's Eve celebrations - urging the public to take precautions as they do so.
"I think everybody should enjoy New Year but in a cautious and sensible way," the prime minister said on Wednesday.
"Take a test, ventilation, think about others - but above all, get a booster."
While the government's booster programme has been record-breaking, it has come under criticism over its guidance on testing due to widespread reports of shortages in PCR and lateral tests. On Thursday, the Labour-run Welsh parliament announced it would loan 4m tests to England amid shortages.
Wales, Scotland and Northern Ireland have introduced new restrictions in response to the new variant such as the closure of nightclubs and pleas to keep gatherings small. Welsh first minister Mark Drakeford warned the Welsh public they were "facing a very serious situation in Wales".
And on Thursday, Scottish first minister Nicola Sturgeon urged Scots to follow new guidance and restrictions amid another record breaking day for cases: “As we approach the New Year, I am appealing to everyone to keep following this advice – for your own sake and also to help the NHS."
Deepti Gurdasani, an epidemiologist at Queen Mary University in London, who is also part of the unofficial Independent SAGE group of COVID experts, has criticised the government's decision to continue on its current path.
“We live in a country where the govt will ask the military to set up field hospitals & plan for mortuary capacity before enacting even the most basic public health measures to prevent this," Gurdsani wrote on Twitter.
“183,000 confirmed cases today - the silence is deafening.”
The UK recorded its highest ever number of COVID cases on Wednesday, reporting 183,037 new cases within a 24-hour period and 57 deaths.
Watch: 'Great concern' amid shortage of lateral flow and PCR tests before New Year's Eve