A team from University College London, the University of Cambridge and Health Data Research UK say current measures don't go far enough to stop the spread of Covid-19.
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The group of clinicians, statisticians and epidemiologists also said the government should ditch voluntary measures and instead turn to enforced lockdowns or social distancing.
Their study – reported in the Financial Times but not yet published in a peer-reviewed journal – estimated the excess number of deaths caused by coronavirus in relation to underlying conditions and age.
Using NHS health records from 3.8 million adults in England, they found that between 35,000 and 70,000 people are likely to die as a result of the illness.
Dr Amitava Banerjee of UCL, the lead author, said: “The UK government is currently following a partial suppression policy of population-wide social distancing, combined with home isolation of cases, as well as school and university closures, but this is currently not [mandatory].
“Our study indicates that the government should implement more stringent suppression at population level to avoid not just immediate deaths but also long-term excess deaths."
He added that the research takes into account the fact that some people would have died from other causes.
So far, in the UK, all of those who have died from Covid-19 were either elderly or had an underlying health condition.
The government's chief scientist, Patrick Vallance, last week said that a UK death toll of around 20,000 would be a "good outcome".
Meanwhile, the Prime Minister dramatically ramped up the government's response to tackle the virus after modelling showed that there could be hundreds of thousands of deaths.
But Boris Johnson has come under pressure to introduce tighter controls after Brits flocked to parks and beaches at the weekend, while commuters crammed onto trains this morning.
'Suppression efforts won't prevent deaths'
But not everyone agrees an enforced lockdown would reduce the number of deaths due to Covid-19.
Responding to the new preprint paper, Prof Robert Dingwall, from Nottingham Trent University, said: “Suppression efforts would not prevent deaths, merely delay them, and it is misleading to imply otherwise.
"What the paper shows is that Covid-19 is probably going to bring forward a lot of deaths that would have occurred anyway in the next 12 months.
Covid-19 is probably going to bring forward a lot of deaths that would have occurred anyway in the next 12 months
"At a population level, however, we can reasonably ask whether the collateral damage to society and the economy from more aggressive suppression is justifiable.
"If the benefit is so modest, we might also wonder whether it will actually be exceeded by mortality from other causes such as suicides resulting from the mental health impact of self-isolation, cardiac events prompted by the associated inactivity or longer-term mortality resulting from unemployment and reduced living standards.”
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Dr Jennifer Cole, biological anthropologist at the Royal Holloway, University of London, pointed out that the researchers hadn't been given access to NHS data on the Covid-19 epidemic due to privacy concerns.
She added: "Events such as this are precisely why such access to health data is essential.
"This is not about invading privacy or snooping on the population, it is about saving lives.
"The number of excess deaths, the paper concludes, may be dependent on being able to target preventative interventions to those at highest risk.
"Researchers, policymakers and healthcare professionals cannot know which groups or individuals these are without full access to patient data.
"The data analysis also then need to be shared with the public, and explained clearly so that the progression of the disease and its likely impact on individuals is fully understood.”
It comes as the Health Secretary branded those who are ignoring social distancing advice to stay two metres apart as "very selfish".
Matt Hancock also indicated that further measures could be brought in to tackle the virus.
Over the weekend, photos emerged showing crowds of people visiting open spaces across many parts of the UK.
The Government has said it is safe to exercise as long as people keep at least two metres away from other people.
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