The study, by Imperial College London, says the pace of the epidemic is accelerating and estimates the number of people infected is now doubling every nine days.
The authors say we are at a "critical stage" and "something has to change".
France and Germany have turned to forms of lockdown to control the virus.
Communities Secretary Robert Jenrick told BBC Breakfast the government wanted to "try to avoid having a national blanket approach" to coronavirus restrictions in England, where a regional three-tier alert system is in place.
"We don't have a plan, today, to do a full national lockdown," he said, adding such a move "would be destructive to people's lives and livelihoods and broader health and wellbeing".
A national "firebreak" lockdown is ongoing in Wales, while Northern Ireland has tightened restrictions, including closing schools, and Scotland has confirmed details of its new tiered alert system.
Labour's shadow health secretary Jonathan Ashworth called for Prime Minister Boris Johnson to hold a news conference to outline "steps he will now take to get control of the virus and save lives".
Experts are warning that we are fast approaching the peak in infections seen in the spring.
The React-1 study is highly influential because it is the most up-to-date assessment of Covid-19 in the country, with the last swabs taken only on Sunday and nearly 86,000 volunteers taking part.