Fewer than 2,000 people were contacted in the first four days of the NHS Test and Trace scheme, according to a leaked copy of data.

The Government has yet to publish figures, but Channel 4 News has seen the data from Thursday – the day the system was launched – running up to Sunday, and it shows that 4,456 confirmed Covid-19 cases reported to Test and Trace in that period.

Of those, 1,831 self-registered on the website or have been called and completed the form providing information about their contacts.

The number of contacts they provided was 4,634, of whom just 1,749 have been contacted, Channel 4 News reported.

Health Secretary Matt Hancock told the House of Commons on Tuesday that NHS Test and Trace is “working well”, saying: “Thousands of people have been contacted and are being traced, their contacts are being traced so the system is working.

“We absolutely will publish data on that, but as the letter from the chief statistician from UKSA (UK Statistics Authority) shows this morning, it’s very important that we get that data publication right, so we will work with the UK Statistics Authority to make sure they are happy with how we’re publishing that data.”

Mr Hancock was rebuked by the UK’s statistics watchdog over coronavirus testing figures which are “still far from complete and comprehensible”.

UKSA chairman Sir David Norgrove said “it is not surprising that given their inadequacy data on testing are so widely criticised and often mistrusted”.

He criticised the way the figures are presented at the daily Downing Street briefings, with the headline total including tests carried out and those that have been posted to recipients but not yet conducted.

He said it underlined the importance of developing a tracing programme, saying: “The test and trace system that we have built over the past few weeks is one of the lessons that comes out of it – the absolute vital importance of having a system that is big enough to be able to trace as many of those who tested positive as possible.”

Public Health England’s Professor John Newton, the national testing co-ordinator, said: “We are really keen for anybody who has symptoms that might be coronavirus to come forward, have a test, and so we can give a definitive answer. And if they are positive they can be entered into the test and trace programme.

“There are thousands of people who have already tested positive who have been successfully fed into the test and trace programme… using the online tool they have identified contacts.

“And there are thousands of contacts who have been successfully identified and agreed to self-isolate. That programme is going well.”

Contacted about the figures from Channel 4 News, a Department of Health and Social Care spokesman said: “These figures are outdated and fail to reflect the huge amount of work already under way, with thousands of people already contacted in just a matter of days and their contacts successfully traced.

“We are working with the UKSA to finalise the most useful information to publish on its performance and will be providing weekly updates shortly.”