Nearly 16,000 cases of coronavirus were not entered into the national computer system used for official figures because of a technical glitch, Public Health England has said.
Some of the unreported cases were then added to Saturday's figure of 12,872 new cases and Sunday's 22,961 figure.
PHE said all of the cases "received their Covid-19 test result as normal".
But it means there has been a delay in tracing their contacts, who may have been exposed to the virus.
The BBC's health editor Hugh Pym said daily figures for the end of the week were "actually nearer 11,000", rather than the around 7,000 reported.
According to PHE, the cases were missed off daily reports between 25 September and 2 October.
However, it has insisted the IT problem has been resolved and all cases have now been handed over to the test and trace system.
Labour has described the glitch as "shambolic".
Meanwhile, the head of the government's vaccine taskforce, Kate Bingham, has told the Financial Times that less than half of the UK population could be vaccinated against coronavirus.
"There is going to be no vaccination of people under 18," she said. "It's an adult-only vaccine for people over 50, focusing on health workers, care home workers and the vulnerable."
Earlier, Prime Minister Boris Johnson warned it could be "bumpy through to Christmas" and beyond as the UK deals with coronavirus.
Speaking to the BBC's Andrew Marr, the PM said there was "hope" in beating Covid, and called on the public to "act fearlessly but with common sense".
At a time when the testing system has come under intense scrutiny after reports of delays and a system struggling to keep up with demand, the latest revelation could not have come at a more awkward moment for the government at Westminster.
Because the nearly 16,000 extra positive test results had been not entered into the test and trace system, their recent contacts were not immediately followed up.
Experts advise that ideally contacts should be tracked down within 48 hours.
Officials say the technical problem - thought to be IT related - has been resolved, with all the new cases added into totals reported over the weekend.
But all this will hardly improve public confidence in the testing system in England.
And it muddies the waters for policy makers and officials trying to track the spread of the virus at what the prime minister has called a "critical moment".
On Sunday, the government's coronavirus dashboard said that, as of 09:00 BST, there had been a further 22,961 lab-confirmed cases of coronavirus in the UK, bringing the total number of cases in the UK to 502,978.
Another 33 people were reported to have died within 28 days of testing positive for Covid-19 as of Sunday.
A note on the dashboard said: "The cases by publish date for 3 and 4 October include 15,841 additional cases with specimen dates between 25 September and 2 October - they are therefore artificially high for England and the UK."
Public Health England's interim chief executive Michael Brodie said a "technical issue" was identified overnight on Friday, 2 October in the process that transfers Covid-19 positive lab results into reporting dashboards.
"After rapid investigation, we have identified that 15,841 cases between 25 September and 2 October were not included in the reported daily Covid-19 cases. The majority of these cases occurred in the most recent days," he said.
"Every one of these cases received their Covid-19 test result as normal and all those who tested positive were advised to self-isolate."
He said they worked with NHS Test and Trace to "quickly resolve the issue and transferred all outstanding cases immediately into the NHS Test and Trace contact tracing system".
"We fully understand the concern this may cause and further robust measures have been put in place as a result," he said.
Test and Trace and Public Health England joint medical adviser, Susan Hopkins, added that "a thorough public health risk assessment was undertaken to ensure outstanding cases were prioritised for contact tracing effectively".
PHE said NHS Test and Trace have made sure there are enough contact tracers working, and are working with local teams to ensure they also have sufficient resources to be urgently able to contact all cases.
The number of call attempts is being increased from 10 to 15 over 96 hours.
Labour's shadow health secretary Jonathan Ashworth said: "This is shambolic and people across the country will be understandably alarmed.
"(Health Secretary) Matt Hancock should come to the House of Commons on Monday to explain what on earth has happened, what impact it has had on our ability to contain this virus, and what he plans to do to fix test and trace."
A Department of Health spokesman said the issue had not affected people receiving test results, and all those who tested positive had been informed in the normal way.
News of the glitch in the daily count first emerged late on Saturday, when the UK announce.