The health secretary has failed to say whether Dominic Cummings did the right thing when he drove to Durham during lockdown, as he insisted the public must obey government test-and-trace instructions. Asked why the public should follow the new self-isolation rules, when even Conservative MPs believe Boris Johnson’s most senior aide breached them, Matt Hancock said it was in everyone’s interests that “people follow the instructions from the NHS”. The health secretary is launching the government’s test-and-trace system in England on Thursday with 25,000 tracers who will call members of the public if they have been in contact with someone who has tested positive for coronavirus. They will be asked to self-isolate for 14 days even if they do not have symptoms. However, there has been criticism that Cummings’ 260-mile journey from London to Durham, and a second journey to Barnard Castle that he said was to test his eyesight, risks undermining the success of this new programme. Asked repeatedly on BBC Radio 4’s Today programme if Cummings had done the right thing, Hancock said he had answered the question in previous days and the prime minister had responded to “all these questions endlessly”. The show’s presenter, Nick Robinson, said Johnson had never answered “the moral case” on whether Cummings had done the right thing and asked Hancock again if Cummings had done the right thing and his duty. Hancock said: “I’ve said that I think he was acting within the guidelines and I also understand why reasonable people might disagree with that.” He denied he was dodging questions and responded to Robinson: “You asked the question about what’s important. I’ll tell you what’s important – what’s important is all that we can do and are doing to get out of this terrible situation. The best thing people can do is follow the instructions of the NHS.” He said he was determined to make sure the new rules were clearly understood and “land with the public”. The row over Cummings’ lockdown breach has continued, with more than 40 Conservative MPs critical of his actions and calling for his resignation. The Cabinet Office minister Penny Mordaunt said there were inconsistencies in Cummings’ account. Hancock ended his interview with Today by saying: “In this war on the virus, ultimately we are all on the same side and we’ve all got a part that we can play.” The health secretary also laughed off claims during a Sky News interview that the test and trace scheme had been brought in earlier than its original 1 June start date to try and deflect from unrest around Cummings. He said the accusation was “priceless” as he is usually accused of delays and then burst out laughing. Presenter Kay Burley said the track and trace app for mobile phones, which is one part of the strategy and previously described as essential, was promised in mid-May and has still not been rolled out. The shadow health secretary, Jonathan Ashworth, voiced support for the test and trace scheme as “the only way we can safely ease out of this lockdown”, but suggested Hancock’s support for Cummings could undermine public cooperation. He told BBC Breakfast: “We need everybody to cooperate with this because it’s in all of our interests that this works, and I’m sorry, I’ve got to say it, it’s why I think Matt Hancock’s support of Dominic Cummings is really irresponsible. “My worry is some people will think ‘Why should I stay at home for two weeks on my own when I feel fine, while this guy who’s Boris Johnson’s big pal in Downing Street can get away with travelling across the country to Durham?’” The Labour MP also urged the government to return test results within 24 hours, instead of up to five days, to ensure those required to isolate would get sick pay from the start of their quarantine period.