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The government could make the NHS Test and Trace system mandatory if people with coronavirus symptoms refuse to co-operate, the health secretary has warned. 

Speaking at the Downing Street briefing on Thursday, Matt Hancock said he would not rule out enforcing the programme, which helps the government track and control the spread of the virus as the UK moves out of lockdown. 

It came after new figures for NHS Test and Trace, which was set up on June 1, revealed some 33% (2,710) of people who tested positive for Covid-19 failed to provide information on who they had been in contact with. 

Dido Harding, the head of the programme, has admitted Test and Trace is not yet the “gold standard” but Hancock said members of the public should view taking part as their “civic duty”. 

When asked whether enforcement such as fines would be necessary, he added: “We’re not ruling it out but I don’t think we need it at the moment. 

“What we’ve got to do it keep seeing those numbers going up, the numbers of people in the system and the proportion that we get to, because we think that is the best way forward.” 

He also said firms could “mitigate” against the risk that large numbers of employees could be required to self-isolate by ensuring workplaces were safe.

“By being Covid-secure at work, that helps to ensure that fewer people will have to self-isolate if one of the team tests positive,” he told the No 10 briefing.

Amid much criticism that NHS Test and Trace had been rushed into operation and was still flawed, Harding, who appeared alongside Hancock, defended the system as “fit for purpose”. 

She added that the “vast majority” of people were complying with instructions. 

She added: “Making sure that we bring as many people as possible who have got coronavirus into the Test and Trace programme is the number one thing we need to improve over the coming weeks.”

Some 8,117 people who tested positive for Covid-19 in England had their case transferred to the NHS system, of whom 5,407 (67%) were reached, while 2,710 were not. 

Overall, 31,794 contacts were identified and, of these, 26,985 were reached and advised to self-isolate – 85% of the total number of contacts.

Of the remaining 15% (4,809), some were not reached, others said they were already taking action independently of the system and some simply refused to comply. People are contacted 10 times in a 24-hour period.

Harding went on to tell the Downing Street briefing: “Given that it is still early days this is really encouraging, it means that the vast majority of people are responding positively and willingly, sharing information and self-isolating when needed.

“Our first week of data shows this partnership (between the public and the NHS) has got off to a good start but together we know there are further improvements we can make to the system.”

Labour’s shadow health secretary Jon Ashworth had called on Hancock to explain why the service failed to contact 33% of people who had tested positive – and what measures were in place should this trend continue.   

“Tracing is vital to the safe easing of lockdown,” he said. “Though this is early data, Matt Hancock needs to explain at this evening’s press conference why a third of people don’t appear to have been contacted and what action they will take to rectify this.”