Boris Johnson is facing cross-party calls to stop his chief adviser from attending meetings of the secret scientific group advising him on the coronavirus pandemic, as demands grow for the committee’s deliberations to be made public.

The former Brexit secretary, David Davis, is among those calling for Dominic Cummings and Ben Warner, an adviser who ran the Tories’ private election computer model, to be prevented from attending future meetings of the Scientific Advisory Group for Emergencies (Sage).

Davis said that Cummings’s presence could alter the advice offered in meetings, adding: “We should publish the membership of Sage, remove any non-scientist members, publish their advice in full, and publish dissenting opinions with the advice.”

It comes after the Guardian reported that Cummings and Warner were among the 23 who attended Sage on the day Johnson announced the lockdown, and had been able to question attendees at other meetings.

David Davis. Photograph: Rex

There is now a broad coalition forming to demand greater transparency about Sage. Greg Clark, the Tory chair of the Commons science committee, said: “I have great respect for [chief scientific adviser] Sir Patrick Vallance and [chief medical officer] Chris Whitty, the co-chairs of Sage. I am sure the scientists they ask to serve on the group are of the highest calibre.

“For that reason, disclosing who has attended Sage meetings could reassure and enhance the standing of the body whose advice is so important to the country at this time. It would also allow for a better understanding of the range of disciplines which are shaping advice to government.”

Others called for the minutes of Sage meetings to be published. The shadow health secretary, Jonathan Ashworth, said: “It’s vital public confidence is maintained in this process. The membership and supporting papers should be published. Total transparency is crucial.”

The acting Lib Dem leader, Ed Davey, said: “The public needs to have confidence that it is expert advice that is guiding government decisions. The lack of transparency is unacceptable in this national crisis.”

Adam Price, the Plaid Cymru leader, said: “The fact the chief medical officer of Wales couldn’t even ask questions, but Boris Johnson’s chief spin doctor had a place at the table is as shocking as it is wrong. This government needs to start treating people like grown-ups and publish the advice they are receiving.”

Greg Clark. Photograph: Tolga Akmen/AFP via Getty Images

Downing Street reacted furiously to the initial report, adding it was “not true that Mr Cummings or Dr Warner are ‘on’ or members of Sage”. One insider was frustrated that the government was in a no-win situation. Having previously been criticised for delays and complacency, they said they were now being criticised for having senior advisers attend crucial meetings.

Prof Stephen Powis, who is a Sage member and NHS England medical director, said he was confident that what happens at Sage was a “scientific discussion involving the scientists and experts who are members of Sage”.

He added: “The experts, from a variety of backgrounds, discuss the evidence; they discuss the evidence base of the various topics; they come to conclusions around that evidence base,” he told BBC Radio 4’s Today programme. “It is then, of course, the role of Sage to advise the government.”

Asked again at the Downing Street press conference whether Cummings made contributions to Sage, Powis would only say that it is the “scientists that make the scientific contributions”.

Previous scientific advisers said the details of Cummings’s involvement in the committee were crucial. Prof Derek Hill, of University College London, said: “I was on a science advisory group for dementia research when David Cameron was prime minister. Advisers from No 10 often turned up, but just as observers.

“The question here is whether Cummings not only attends but actively participates in Sage. For example, does he talk more at these meetings than some of the scientists?”