The figure, which emerged under questioning from MPs, underlined the sheer scale of untracked spread of the virus as the UK struggles with a highly infectious new variant.
But the Tory peer suggested that paying people more money to quarantine at home may not drive “the right behaviour” and may lead to “unforeseen consequences”.
Giving evidence to the Commons Science and Technology Committee, Harding said that the most recent figure for Covid cases and their contacts was 700,000 people last week.
Pressed by former health secretary Jeremy Hunt to estimate how many were not isolating, she said around 20% – on the best estimates – were failing to do so.
She said with 100,000 total cases and contacts per day, “circa 20,000 people a day would not be” staying at home as they should be.
Hunt said: “Thousands of people every day is enough to restart the pandemic.”
Harding also came under fire for having claimed last year that the £22bn cost of her service would prevent a second and third wave of the pandemic, and was criticised for failing to publish evidence that Test and Trace was having a significant impact on the “R number” that indicates the spread of the virus.
She raised eyebrows, too, when she declared that “none of us were able to predict” the new variants, such as the Kent and South African mutations that have high levels of transmissibility.
Asked by Hunt why she thought people were not isolating when they should be, Harding said one element was communication – people not understanding and not being clear about what they should and should not do.
“The clearer and simpler the guidance, the easier is it for people to follow it,” she said.
She added that cash support was also a factor for low isolation rates, but said any financial incentive should be devised so it “genuinely drives the right behaviour, rather than any unforeseen consequences”.
After the hearing, shadow health minister Justin Madders said: “It has been clear for a year now that many people would need financial support in order to self isolate.
“Now that Dido Harding has set out what that means in terms of people potentially infecting others on a daily basis surely the Government must now come forward with a proper self isolation support scheme.”
Former health secretary Hunt also said that the figures laid bare “a gaping hole” in financial support.
During the session, committee chair Greg Clark put to Harding that Test and Trace’s business case published last year had sought to justify its huge £22bn budget by saying its “main driver” was “the avoidance of a second national lockdown and the vast associated social and economic costs”.
Harding replied: “We are not the single silver bullet. Between that business plan being published and us going into the lockdown we’re currently in now, we’ve seen the virus mutate, we’ve seen the new variants emerge, which was something that none of us had were able to predict.”
Clark later picked up on that claim. “Was it not possible, is it not possible, to be primed and ready to respond actually to mutations, which most scientists we’ve heard from across the year have felt was not only likely but almost certain?”
Harding replied that extra “surge capacity” in her service had proved it was ready deploy genomic sequencing to spot new variants.
“What I was referring to earlier is predicting exactly when that is going to happen, and therefore being ahead of the curve – that’s much harder. And I don’t think any scientists in the world would be willing to sign up to a date stamp of when specific mutations are likely to occur.”
During evidence, Harding confirmed that private consultants had been hired at a pay rate of £1,100 a day. Test and Trace testing director Mark Hewlett revealed that approximately 200 private consultants would be replaced in the next three months by full-time civil servants.