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Boris Johnson has refused to publish the evidence Dominic Cummings gave him to save his job after he apparently breached coronavirus lockdown rules.

Under pressure from Labour’s Meg Hillier, the prime minister claimed he had seen evidence that showed some of the allegations about his senior aide were false.

In an extraordinary Monday press conference, Cummings admitted the central claims – that he drove 260 miles to Durham during lockdown and took a trip to Barnard Castle.

Johnson said he had seen evidence that other claims made were false.

But he refused to publish or hand it to cabinet secretary Sir Mark Sedwill, the head of the civil service, to probe the adviser’s actions.

The PM told the Commons liaison committee: “It would not be doing my job if I were now to shuffle this problem into the hands of officials who believe me, as I think the public would want, are working flat out to deal with coronavirus. 

Johnson also denied that the public are now less likely to abide by restrictions because of Cummings’ actions despite polls suggesting they are more likely to flout the rules.

Conservative MP Simon Hoare told the PM the nation will be “far less energetic” about obeying future restrictions as “a direct result of the activities of your senior adviser”.

Hoare asked what MPs should tell constituents who ask: “If other people don’t abide by it, why on earth should we?” He added: “We know what your views are. Frankly, prime minister, I don’t think anybody understands why you hold those views.”

Johnson replied: “I don’t think that’s true about how the British people will respond to the next phases, to how to work the test and trace system – I don’t think that’s how they responded at all throughout the crisis.

“If, just suppose for a second that you were right, which I don’t accept, all the more reason now for us to be consistent and clear in our message driving those key messages.”

Labour’s Yvette Cooper meanwhile asked Johnson to clarify the instructions to parents with coronavirus symptoms who have no local childcare, after Cummings claimed he had to travel to Durham in case someone needed to look after his child.

The PM denied there was a conflict between how Cummings interpreted the rules compared to parents who stayed at home during the lockdown despite having the virus or its symptoms.

Asked by Cooper whether parents with coronavirus who could not access childcare locally should travel across the country like Cummings or stay at home, Johnson said: “I think we’d have to look at each individual case and the particular circumstances that my adviser explained.”

Johnson also refused to apologise for the affair, which has hit Tory poll ratings and triggered a revolt of dozens of the party’s MPs.

He instead apologised for the wider “hurt and pain” the Covid-19 crisis has caused.

“I, of course, am deeply sorry for all the hurt and pain and anxiety that people have been going through throughout this period – this country has been going through a frankly most difficult time,” Johnson said. 

“We are asking people to do quite exceptionally tough things, separating them from their families.”