Video report by ITV News Health Editor Emily Morgan
The issue, which relates to technical error with an Excel spreadsheet, stopped almost 16,000 new cases from being reported, and as a result, thousands of their contacts were not told to self-isolate by NHS Test and Trace.
Health Secretary Matt Hancock admitted the incident "should never have happened" but said the assessment of the Covid-19 pandemic had "not substantially changed" due to the new data.
He said 6,500 hours of additional tracing had been brought in over the weekend to trace all potential contacts but said that 49% had still not been contacted as of 9am on Monday.
Labour's shadow health secretary Jonathan Ashworth said it "means as many as 48,000 contacts not traced and not isolating".
"Thousands of people blissfully unaware they’ve been exposed to Covid potentially spreading this deadly virus at a time when hospital admissions are increasing and we’re in the second wave.
“This isn’t just a shambles, it’s so much worse than this and it gives me no comfort to say it, but it’s putting lives at risk and he should apologise when he responds.”Mr Hancock said he would ensure the issue "never happens again ", adding that the "serious issue" is being "investigated fully".
Mr Hancock insisted that everyone who was tested was "told that result in the normal way in the normal timeframe".
"They were told that they needed to self-isolate, which is of course now required by law.
"However, these positive test results were not reported in the public data and were not transferred to the contact tracing system."
He added: "Control in care homes, schools and hospitals has not been directly affected because dealing with outbreaks in these settings does not primarily rely on this PHE system."
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The recording error - which Mr Hancock said happened "due to a failure in the automated transfer of files from the labs to PHE's data systems" - caused daily coronavirus infections to reach their highest point ever when the missed cases were added to the system.
On Sunday, a huge 22,961 new cases were reported, bringing the UK's total number of confirmed cases to 502,978.
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By Monday, the new daily cases in the UK dropped to 12,594.
Boris Johnson, when asked about the testing issue, was unable to confirm how many potential coronavirus contacts had been missed as a result.
"I can't give you those figures," he said, "what I can say is all those people are obviously being contacted and the key thing is that everybody, whether in this group or generally, should self-isolate."
Explaining the missing cases, he said: "What happened here was that some of the data got truncated and it was lost.
"But what they have done now is not only contacted all the people who were identified as having the disease - that was done in the first place - but they are now working through all the contacts as well."
The Health Secretary also outlined measures to improve how quickly new drugs can be given to UK patients.
He explained: "The UK is joining with Canada, the United States, Australia, Switzerland and Singapore in Project Orbis, which will allow international regulators to work together to review and improve the next generation of cancer treatments faster.
"This means pharmaceutical companies can submit treatments to be reviewed by several countries at the same time so that we can co-operate with the best medical regulators in the world and make approvals quicker, so we can get patients the fastest possible access to new drugs."
Mr Hancock said the UK will fully join the scheme on January 1 next year, once the Brexit transition period ends.