Boris Johnson is being urged by senior Tories to come clean about the funding of his flat refurbishment as it emerged that a former Labour chancellor refused to join a trust overseeing Downing Street upkeep out of concerns it could lead to a cash-for-access scandal.

The prime minister faced growing disquiet from within his own party on Tuesday over allegations that he was loaned £58,000 from Conservative party funds while being seen to personally foot the bill for renovations of his Downing Street residence.

Reports have alleged that the refurbishment was initially paid for by a donation from Tory peer and donor Lord Brownlow to Conservative campaign headquarters (CCHQ), which then loaned the money to Johnson.

No 10 has insisted that “Conservative party funds are not being used to pay for the Downing Street flat” but have not denied the existence of a donation or loan arrangement. Labour has demanded a formal investigation into whether the government was trying to orchestrate a “cover-up”.

It comes as Johnson faced pressure on a number of fronts, including claims that he said he would rather see “bodies pile high” than order a third coronavirus lockdown last year.

On Tuesday the Guardian confirmed that Alistair Darling turned down an offer to be a member of a new trust to refurbish No 10 and No 11 Downing Street, citing concerns about the potential for donors to expect political favours.

After being approached through the office of Labour leader Keir Starmer in July, Darling is said to have expressed concern about the plans – first due to a belief that the state has a duty to maintain the iconic buildings and second because of what he saw as a significant risk of cash for access.

The head of the civil service, Simon Case, confirmed on Monday that the idea of a trust had been looked into but would not have worked. “A charitable trust can’t cover private areas of Downing Street, so that’s clear that that can’t be done,” he told MPs.

The full cost of the refurbishment works has not been confirmed but is thought to have gone well above the £30,000 cap available for premiers to claim taxpayers’ money. No date has been set yet for when the Cabinet Office will publish its annual accounts or the register of ministers’ interests, which is expected to shed light on the funding.

The ministerial code stipulates that ministers “must ensure that no conflict arises, or could reasonably be perceived to arise, between their public duties and their private interests, financial or otherwise”. The Electoral Commission is considering opening a formal investigation into whether all donations were properly declared by the Conservative party.

On Friday Johnson’s former chief of staff Dominic Cummings revealed that he had been deeply opposed to soliciting donations for the flat’s refurbishment. Cummings claimed he warned Johnson that the plans were “unethical, foolish, possibly illegal and almost certainly broke the rules on proper disclosure of political donations if conducted in the way he intended”.

On Tuesday a cabinet minister said that, while they detected little public pressure on the issue, giving Johnson some room for manoeuvre, there was a feeling that clarity would now help. “My view has always been that start with the truth, that’s where you’ll end up anyway,” they urged.

Some Tory MPs railed privately at their party and raised questions about co-chair Amanda Milling, who said less than a month ago that “Conservative party funds are not being used to pay for the Downing Street flat”.

The same claim was made by the prime minister’s former press secretary Allegra Stratton about the residence, where Johnson lives with his fiancee, Carrie Symonds, and their son.

Tory MPs said there could be an innocent answer to how Johnson footed the costs but that a lack of proof was making things worse. “There’s a reasonable set of questions that need to be answered – our position at the moment isn’t ideal,” one said.

Concern is also rising that while the issue may not have had significant cut-through with the public yet, it may in the days ahead, including in the run-up to elections on 6 May.

A senior MP said: “Broadly I do think the ‘he said/she said’ stuff just turns everybody off politics full stop, and generally the mood is positive. But after a while the general atmosphere – rather than the specific details – around trust start to seep out. I sometimes wonder who is actually working for the PM and who is working for their own little tribe. It will need a long-term fix, not a quick one.”

Caroline Slocock, former private secretary to Margaret Thatcher who now runs the Civil Exchange thinktank, told the Guardian she was “concerned” about any donors “paying for work which the prime minister should be paying for”, adding: “We do appear to have a very un-transparent situation here, which is a problem.”

Labour’s deputy leader, Angela Rayner, has demanded that Case investigates Stratton’s denials last month that Tory funds were used to help pay for the renovations. Case revealed on Monday that he has opened an inquiry into the matter, and Rayner said it should include whether Stratton had broken the civil service code on acting with honesty and integrity.

He was urged by Rayner to look into whether Stratton “knowingly misled journalists and the public, or was misled herself by senior members of the government who seem intent on a cover-up”.

No 10 said: “Any costs of wider refurbishment this year beyond those provided for by the annual allowance have been met by the prime minister personally. Conservative party funds are not being used for this.”

A Conservative party spokesperson added: “All reportable donations to the Conservative party are correctly declared to the Electoral Commission, published by them and comply fully with the law. Gifts and benefits received in a ministerial capacity are, and will continue to be, declared in Government transparency returns.”