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There is widespread growth of the epidemic across the country and the R number has risen to between 1.1 and 1.4, say the government's scientific advisers.
Officials are warning of "far worse things to come" as cases are thought to exceed 6,000 a day in England.
And the scientist behind the Covid Symptom Study app said it appeared to be "the start of a second wave".
The developments come as new England-wide restrictions are being discussed.
At least 13.5 million people, roughly one-in-five of the UK population, are facing some form of local restrictions.
Cases of the virus and hospital admissions for Covid-19 are thought to be doubling every seven to eight days in the UK.
Although deaths remain at very low levels, Sage, the scientific body which advises the UK government on the epidemic, says the rise in the R number "shows that we are moving to wider spread growth in transmission at a faster rate".
This follows a sharp rise in new daily UK lab-confirmed cases to 3,395 over the last two weeks and ongoing problems with the government's test and trace programme, leading to people struggling to access tests.
'Worrying picture'
Yvonne Doyle, medical director at Public Health England said there were "clear signs the virus is now spreading widely across all age groups", adding she was particularly worried "by the increase in rates of admission to hospital and intensive care among older people".
The Covid Symptom Study app, which tracks the health of four million people in the UK, estimates there are around 7,500 new cases of Covid every day over the last two weeks.
Their latest figures show a rise in cases in London for the first time since June.
Prof Tim Spector, professor of genetic epidemiology at King's College London and app founder, said it was "a worrying picture", adding it appears "to be the start of a second wave".
The ONS infection survey, which covers the week to 10 September and tests thousands of people in random households whether they have symptoms or not, estimated there were around 6,000 new infections a day.
It found infection rates were highest in the North West and London, and children aged two to 11 and young people aged 17 to 34 had most positive tests.
ONS data from Wales suggests Covid-19 cases there are currently "relatively stable" - with an estimated one in 2,000 people testing positive.
But the ONS said the results in Wales should be interpreted with caution because of the small number of tests in the sample.
