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.
The UK government is sticking to its regional strategy in England.
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.
It shows cases are rising in every age group and in every region of England.
While cases are currently highest in the North, infections are surging more rapidly in the South.
The study compared the latest swabs collected between 16 and 25 October with the last round of swabs, between 18 September and 5 October.
The number of people infected has more than doubled since the last round, with one in every 78 people now testing positive.
The hardest hit area is Yorkshire and the Humber, where one every 37 people has the virus, followed by the North West region.
Three times as many people aged 55-64 are infected and twice as many over 65s.
The pace of the epidemic has accelerated with the R number - the number of people each infected person passes the virus on to on average - increasing from 1.15 to 1.56.
Overall, the number of people infected is doubling every nine days
The South East, South West, east of England and London all have an R above 2.0. London has an estimated R of 2.86.
Cases are spiking in young people in the South West in a repeat of the pattern seen in northern England just over a month ago.
96,000 people are now catching the virus every day.
Prof Steven Riley, one of the authors, said he was "really disappointed" when the data started coming in and said it meant the "current measures are not sufficient".
"There has to be a change, the rate of growth is really quite rapid, one way or another there has to be a change before Christmas," he said.
He argued this could be either the general public following the rules more closely or government imposing tougher restrictions on our lives.
"If we are going to consider at some point over the winter something much more stringent it becomes a question of timing. I think these results do argue for something sooner rather than later," Prof Riley said.
Analysis: Stark picture of a challenging winter
This study paints a stark picture of where we are and where we could be heading.
If there was no change in the reported nine-day doubling time, there would be more than a million infections a day by the end of November.
That is a considerable "if", but it demonstrates the threat posed by the virus if it is allowed to grow exponentially.
Somehow, we have to navigate a challenging winter, balancing the virus and the cost of restrictions.
France and Germany have turned to forms of lockdown, albeit not as severe as those endured earlier in the year. The government here is sticking to its regional strategy.
But the hardest fact to digest today may be that it is still only October.
Spring, when hopefully the weather and vaccine will make the virus easier to control, is still a long way away.
Prof Paul Elliott, another report author, said "we're at a critical period in the second wave" and that higher cases "will lead to more hospitalisations and loss of life".
He said we have to cut the number of people we interact with to curb the spread of the virus.
The government is still hoping its local, targeted restrictions will work, allowing more of the economy to stay open in areas where the virus is less prevalent, according to BBC political correspondent Nick Eardley.
But it has also been at pains to say it is ruling nothing out if the virus is out of control - including nationwide measures, he added.
It comes after the environment secretary said "it's too early to say" what Covid rules will be in place by Christmas.
George Eustice warned people "may not be able to get together in the larger groups that they normally would".
The government's coronavirus dashboard reported a 310 further deaths across the UK on Wednesday.
But there were glimmers of hope in the report. Cases in the north east of England are still growing, but much more slowly than before.
And in the North East and Yorkshire and the Humber, the number of 18-24 year olds catching the virus is starting to fall, although it is rising in older age groups.