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The head of the NHS Test and Trace programme in England has admitted the scheme is not yet “gold standard” as figures revealed thousands of people who tested positive for coronavirus did not provide details of their recent contacts.

According to data published on Thursday, some 5,407 out of 8,117 people who tested positive for Covid-19 between May 28 and June 3 provided details of recent contacts.

And the figures showed of 31,794 contacts who were identified over the period, 26,985 were reached and advised to self-isolate.

Baroness Harding, who leads the scheme, said it was not yet at the “gold standard” but said it was now a “functioning service”.

“I have repeatedly said this is the cherry on the cake not the cake itself. And what you’re seeing today is the baking of the cake is going reasonably well,” she added.

Boris Johnson had promised the UK would have a “world-beating” test and trace programme by the start of June.

The scheme, rolled out last month, is seen as an essential tool suppressing coronavirus and returning the UK to something approaching normal life.

People who test positive for coronavirus are contacted and asked about their recent interactions – people they have been in direct contact with or been within two metres of for more than 15 minutes.

Those identified as having been in close contact with someone who has had a positive test must then stay at home for 14 days, even if they do not have symptoms, to stop unknowingly spreading the virus.

The NHS data showed of those people who were reached and asked to provide information about their contacts, just over three-quarters (79%) were contacted within 24 hours of their case being transferred to the Test and Trace system.

Some 14% were contacted between 24 and 48 hours, 3% between 48 and 72 hours, and 4% were contacted after 72 hours.

Harding said: “Just as the infection rate is coming down in the country, so is our capability to test and trace growing.

“We have got real scale – this is a national-level service that has stood up in extraordinary time.

“Is it completely perfect? No, of course it isn’t. Is there stuff that we all need to do better? Yes there is.

“But I think it’s fit for purpose as we stand today and will get better through the summer.”