Last Saturday, 3,398 cases were recorded, and seven deaths.
On Friday, 6,238 cases were recorded - the highest number in two months.
A rise in coronavirus cases sparked by a surge of the Indian variant has led the government to consider delaying the planned easing of restrictions in England by two weeks, reports suggest.
Data also showed more than 40 million people have received at least one dose of a Covid vaccine.
A total of 40,124,229 have received their first jab, while some 27,160,635 people have received their second.
Public Health England said on Thursday that the Indian variant is now believed to be dominant in the UK.
Professor Stephen Reicher, a member of the Scientific Pandemic Insights Group on Behaviours (Spi-B) which advises the Government, said that pushing ahead with full reopening later this month would be “foolish”.
He said there is currently enough evidence to say that due to the spread of the Indian variant one of the Government’s four key tests for its road map out of lockdown has not been met.
“I think by the Government’s own criteria it’s quite clear that it would be foolish to proceed on the data that we’ve got at the moment. The risk would be very great indeed,” he said.
“Again, I make the point that it is about data not dates, and if you make it too much about the dates then you box yourself into a corner and I think that’s what the Government has done.”
A UK Government spokeswoman said “no decision” had been made on whether to ease all coronavirus restrictions on June 21.
“As the Prime Minister has set out, we can see nothing in the data at the moment to suggest that we need to deviate from the roadmap,” said the spokeswoman.
“We continue to look at the data and the latest scientific evidence and no decision on Step 4 has yet been made.”
Surge testing has been deployed in 25 areas of the UK to identify both the South African and Indian variants.
On Saturday, multiple reports suggested plans to lift restrictions could be scaled down, with social distancing and the wearing of face coverings set to continue.
However, while case rates have increased, hospitalisations and deaths have remained low, indicating that the vaccination programme is preventing serious illnesses.
Chris Hopson, the chief executive of NHS Providers, said the number of people in hospital with the Covid-19 variant first detected in India, also known as the Delta variant, was not increasing “very significantly”.
He told BBC Breakfast on Saturday that the number of people in hospital in Bolton with Covid-19 peaked at 50, compared to 170 in November and 115 in January and February.
“Infection rates have been increasing in a number of different places,” he said.
“We know that the hospitalisations are increasing, the rates of people coming into hospital in those areas are rising. But they are not rising very significantly.”
He added: “Areas that were at the front of this wave, areas like Bolton, what’s particularly interesting is that they have now got to the point where their community infections have started to decline.”