No 10 is facing growing calls to end the secrecy around the scientific advisory group for emergencies (Sage), which provides the prime minister with evidence about the coronavirus response and how the UK’s lockdown is working.

The group of scientists, which is meeting this week to review lockdown measures, does not disclose its membership beyond that it is chaired by Sir Patrick Vallance, the chief scientific officer, and attended by Prof Chris Whitty, chief medical officer for England.

It published a selection of key papers relating to evidence for the lockdown and physical distancing measures on 26 March – but these are at least a month out of date. No 10 said on Tuesday it was not aware of any plans by Sage to publish more papers or minutes relating to its advice.

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Boris Johnson’s spokesman said there was information about the group on the government’s website and its members were “not hard to find”, as some of them have been interviewed in the media.

However, only a handful of those who sit on the group have publicly revealed themselves to be members, including Sir Jeremy Farrar, director of the Wellcome Trust, who said on Sunday that the UK could have the highest coronavirus death rate in Europe.

Greg Clark, the Conservative MP and chair of the science and technology committee, is one of those pressing for the full membership list to be made public in the interests of transparency. He said one of the main concerns was that “the composition of Sage, and the disciplines represented therein, remains largely unknown”.

Vallance sent him a letter saying the committee was not prepared to reveal its composition because of security advice from the Centre for the Protection of National Infrastructure and to protect members from “undue influence”.

In the letter, he said: “Members of Sage and the expert groups come from over 20 different institutions and have the following areas of expertise: molecular evolution, epidemiology, clinical science and practice, modelling emerging infectious diseases, behavioural science, statistics, virology and microbiology.

“Other Sage participants include the chief medical officer, Public Health England, medical director for NHS England, the Office for National Statistics, the NHS, the Food Standards Agency, Health and Safety Executive, and chief scientific advisers of government departments relevant to specific meetings or their own scientific expertise.”

He said the body had met nine times in February and 10 times in March. But the last minutes published by Sage related to meetings in August 2019 in relation to the breach of a reservoir.

Johnson and his ministers have repeatedly said they are listening to the scientists at all points when implementing their response to coronavirus, but experts have questioned why more public health experts do not seem to be involved in Sage and its subcommittees. Most of the reports feeding into the Sage documents published on 26 March were provided by behavioural scientists and pandemic modellers.

The strategy on tackling coronavirus also appears to have changed several times, including the abandonment of a presumption of herd immunity in favour of trying to suppress the virus, the admission that mass testing of the population will be necessary to exit the lockdown, and the decision to review advice on the wearing of face masks in public.

With pressure mounting on the government to set out an exit strategy on how to ease the lockdown, Jonathan Ashworth, the shadow health secretary, said: “Ministers must be fully transparent about the modelling and evidential base they are using to maintain public confidence. I urge government to publish any outstanding information and papers that have not yet been released.”

Layla Moran, the Liberal Democrat leadership contender, also called for transparency around the membership. “The composition of Sage and the data on which recommendations are being made must be published, so that we can scrutinise and hold ministers to account on their decisions,” she said.

“The tone and quality of the debate improved dramatically following the publication of the Imperial College modelling, on which decisions were being made. Transparency in decisions is the key to keeping the public onside. I see no reason why this information should be hidden in the way that it has so far.”

No 10 denied the set-up lacked transparency. Johnson’s spokesman said: “Sage is obviously a government advisory panel … We are transparent and you are able to scrutinise the most senior members of Sage about the decisions they reach [through the daily press conferences at which officials appear alongside ministers].”

The government is expected to take the decision to extend the lockdown on Thursday, with no relaxation in the measures expected for several weeks. Johnson is continuing to recuperate at Chequers, the prime minister’s country residence, after spending a week in hospital with coronavirus and is not currently working, so Dominic Raab, the foreign secretary, is taking the lead on the process.

Ahead of that, Keir Starmer, the Labour leader, urged the government to publish its exit strategy from the lockdown this week, as he warns that the “silent pressures on families and communities across the country cannot be underestimated”.

He said: “The question … is no longer about whether the lockdown should be extended, but about what the government’s position is on how and when it can be eased in due course and on what criteria that decision will be taken.

“We agree the measures need to remain in place, but to maintain morale and hope, people need a sense of what comes next. The silent pressures on communities across the country cannot be underestimated.”

• This article was amended on 16 April 2020. An earlier version carried a photograph of the national medical director for NHS England, Stephen Powis, which was misidentified as a picture of Patrick Vallance.