Setting up a trust to fund the upkeep of Downing Street has been looked into – but it would not be able to pay for refurbishments to the Prime Minister’s flat, according to the Cabinet Secretary.

Boris Johnson is under pressure about renovations to his No 11 living quarters after his former aide, Dominic Cummings claimed the Prime Minister wanted donors to “secretly pay” for the work in a move which would have been “unethical, foolish, possibly illegal”.

Last week, the Daily Mail published details of an email from Tory peer Lord Brownlow in which he said he was making a £58,000 donation to the party “to cover the payments the party has already made on behalf of the soon-to-be-formed ‘Downing Street Trust’”.

To date, no such trust has been formed, but Cabinet Secretary Simon Case told MPs he had been examining such a concept for the historic government buildings.

Appearing before the Public Administration and Constitutional Affairs Committee, the head of the Civil Service said at present there is a budget of up to £30,000 per year for prime ministers to renovate their Downing Street residency, with any costs beyond that met privately by those in office.

He continued: “On the question of a trust, there has been work on this for more than 12 months.

“Chequers and Dorneywood are actually supported by trusts or a charitable trust and equivalent buildings around the world, like the White House I understand, is supported by a trust.

“No Downing Street trust currently exists. Work was begun last spring.

“Lord Brownlow agreed to be chair of a putative trust. There was work done to identify cross-party potential trustees.”

But Mr Case added: “The first thing I would say is that a charitable trust can’t cover private areas of Downing Street, so that’s clear that that can’t be done.”

The comments come after a senior Government minister insisted Mr Johnson was not “sleazy” as questions continued about how the refurbishment of his Downing Street flat was paid for.

While visiting Wrexham on Monday, Mr Johnson did not deny discussing using donors to fund the work, saying: “If there’s anything to be said about that, any declaration to be made, that will, of course, be made in due course.”

That assertion was backed up by Mr Case, who told MPs on Monday: “All of this will be declared in the proper way.

“The Prime Minister will make relevant declarations.”

The UK’s most senior civil servant, pressed on whether private donations were used to fund the work, said he did “not have all the facts and details at my disposal on this” and said he had been tasked by Mr Johnson to carry out a review.

Earlier on Monday, Defence Secretary Ben Wallace said Mr Johnson had paid “out of his own pocket” for the flat upgrades.

He told BBC Radio 4’s Today programme: “Do I think the Prime Minister is sleazy? No, I don’t.

“He paid out of his own money to refurbish the flat. He paid for his flat.”

Labour has called for a full investigation by the Electoral Commission into the situation.

The commission, which first raised the issue with the Conservatives more than a month ago, confirmed at the weekend it was still looking into whether any of the sums relating to the work on the flat should have been declared.

Labour leader Sir Keir Starmer said: “It’s very important we have answers.”

“It’s all very well the Prime Minister saying, now, ‘well, I paid for it’,” he added.

“The critical question was what was the original arrangement and why is it so complicated?

“If there’s a straightforward answer, then give it.

“If there isn’t, then there are very serious questions to be asked.”

Mr Wallace said the Conservative Party leader had “complied at all stages with the rules”, adding: “We have engaged with the Electoral Commission and we will continue to engage with that.”