More than 103,000 people in England are estimated to have had coronavirus in the week ending 19 September, according to the Office for National Statistics.
The figure is almost double the previous week (4 to 10 September) when it was 59,800.
It equates to around one in 500 people testing positive for COVID-19, according to the ONS, up from around one in 900 the week before.
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There were around 9,600 cases per day during the week until the 19 September – up from 6,000 a day from the previous week, according to the organisation.
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Wales' infections were estimated to have risen seven-fold, going from 1,500 to 10,800 – and equating to one in 300 people.
The numbers are for infections recorded in the community and exclude hospitals, care homes and other institutional settings.
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The ONS said there was evidence of higher infection rates in England's North West, Yorkshire and the Humber, London and North East.
It said the West and East Midlands were also showing a small increase.
The survey covers Northern Ireland for the first time, where the ONS estimated around one in 300 people had the virus there in the two weeks up to 19 September.
Scotland isn't covered by the weekly study, but on Friday the country set a record for new daily cases.
First Minister Nicola Sturgeon said 558 people had tested positive in the past 24 hours, taking the total number since the pandemic began to 26,518.
It comes a day after NHS England launched its contract tracing app, where users have access to postcode district risk level alerts.
The app has revealed that no local area in England is considered a low-risk location, "to reflect the general increase in infection rate across the country," according to the NHS.
In areas with high risk levels, the local authorities – or a neighbouring local authority – is deploying additional measures to reduce the rate of transmission, such as a local lockdown.
The national list in England most recently only highlighted 44 areas of intervention, with three on enhanced support and 11 marked as being of concern.
More than a million downloads of the app among Android users have been recorded on the Google Play Store, with the Department of Health expected to announce exact download numbers on Android and iOS on Monday.
Friday's data was revealed after a joint statement from the UK nations confirmed the start of a second wave – and after the coronavirus alert level was raised from 3 to 4.
The statement said: "Cases are rising rapidly and we must take action to stop an exponential increase that could overwhelm our health services and aim to bring R back below 1 while minimising the impact on the economy and society."
A group representing London's councils also said the capital was now on the national coronavirus watchlist.
Analysis: 'We should be careful about jumping to conclusions'
By Rowland Manthorpe, technology correspondent
The Office for National Statistics survey is probably the best source of infoRead More – Source
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