Public Health England said 15,841 cases between 25 September and 2 October were left out of the UK daily case figures.
They were then added to Saturday's figure of 12,872 new cases and Sunday's 22,961 figure.
PHE said all those who tested positive had been informed. But it means others in close contact with them were not.
The issue has been resolved, PHE said, with outstanding cases passed on to tracers by Saturday.
The technical issue also means that daily totals reported on the government's coronavirus dashboard over the last week have been lower than the true number.
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 7000 reported.
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."