MPs have written to Dominic Cummings demanding that he provide proof for a number of serious allegations against the health secretary, Matt Hancock, who will face a parliamentary inquiry on Thursday. Cummings, who left his post as Boris Johnson’s most senior aide last year, spoke to a joint committee inquiry into lessons learned from the Covid outbreak last month where he repeatedly said Hancock should have been sacked for incompetence and dishonesty. Cummings said during the hearing that he would hand over further written information to substantiate several claims, including that the former cabinet secretary, Mark Sedwill, told Johnson in mid-April 2020 that he had “lost confidence” in the “honesty” of Hancock. In a letter from the committee chairs Greg Clark and Jeremy Hunt, seen by the Guardian, the MPs set out key claims that they ask him to back up with evidence. “During the session you made several commitments to provide us with further documentary information; you also made several serious allegations for which we have requested you provide any evidence you might hold,” they wrote. They said that if evidence could not be provided, the claims would be seen as “unsubstantiated”. The MPs requested evidence for claims including: That Hancock was briefed by the government’s chief scientific adviser Sir Patrick Vallance that not all Covid patients received the treatment they needed. That Sedwill lost confidence in Hancock, about which Cummings said he had made a contemporary note. Allegations that Hancock interfered with testing capacities during April in order to hit targets. That Hancock gave assurances patients were being tested before being discharged from hospital into care homes. The letter also requested that Cummings provide messages he had promised to show the committee, including texts with Hancock in January about pandemic preparedness, as well as relevant exchanges with the prime minister, officials and journalists. “Before the session you also tweeted about a ‘crucial’ document you would give to the committees. We would be grateful to receive that document,” the letter said. It also asked Cummings for evidence for a number of other claims, including that officials believed the UK would not accept an “east Asian-style” test-and-trace system, that the prime minister obstructed a tighter border regime, as well as evidence that Johnson ignored scientific advice in the run-up to the autumn lockdown. No 10 insiders have privately cast doubt on the former aide’s ability to supply watertight evidence for his claims. One former colleague of Cummings said they did not believe there was a “smoking gun” document that would condemn Hancock, saying that emails and texts would add weight to what Cummings said in his evidence rather than reveal new information. Crucial discussions happened in cabinet room meetings between a select group of ministers and staffers and, particularly the PM’s own rogue behaviour, were all mostly in person, the insider said. Questions to be put to the health secretary in the hours-long evidence session on Thursday were expected to include how and when decisions about the first, second and third national lockdowns in England were made, the government’s pandemic preparedness, the impact of the Delta variant discovered in India and Johnson’s roadmap. The letter gave a deadline of last Friday but Hunt confirmed on Tuesday that no additional information had been received. “We haven’t received the written evidence to back those claims up that we were expecting,” he said. He said Cummings “made some very serious allegations” against Hancock and promised to put those claims to the health secretary, when he faced the same committees on Thursday, “to give him his rightful chance to respond”.