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”.