A minister has rejected calls for beefed up powers for an “unelected, unaccountable” ministerial standards adviser, currently looking into the funding of Boris Johnson’s Downing Street flat.

Speaking to Sky News, Victoria Atkins said the suggestion had “not really been thought through”.

She was responding to concerns that the newly-appointed ministerial standards adviser Lord Geidt is unable to properly hold members of the government, including the prime minister, to account.

Lord Geidt does not have the power to launch his own investigations and Number 10 has confirmed the prime minister remains the ultimate judge of any breaches.

Labour has criticised the arrangement, arguing it means Mr Johnson “effectively marks his own homework”.

Opposition criticism has been further fuelled after the PM declined to commit to immediately publish in full any findings from Lord Geidt.

He has been tasked with “ascertaining the facts surrounding” the renovation of Mr Johnson’s No 11 residence and advising him “on any further registration of interests that may be needed”.

Mr Johnson has said he “personally” paid for the refurbishment but has refused to say whether he received an initial donation from the Conservative Party to cover the costs reported to be up to £200,000.

Reacting to demands for a stronger, independent role for the ministerial standards adviser, Ms Atkins insisted that it was right for the PM to have the final say.

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She told Sky News: “He must have control over who is in his government. He’s answerable for their actions. It seems to me the consequences of some of these suggestions that have been flung around in the press haven’t really been thought through.

“I am not sure anyone wants an unelected, unaccountable adviser – impeccable with all of the integrity Lord Geidt has – I am not sure that is an addition to our constitution that we want to walk into without fully understanding the consequences.”

Tory former cabinet minister Lord Lilley also said Parliament should be “very cautious” about the introduction of an independent investigator on ministerial standards.

He told Times Radio: “We must be careful about setting up people who have got power, sovereign power ultimately, to damage who governs us – to decide who governs us, who’s elected or who’s a minister.

“Ultimately, we elect a minister, we elect employees, and MPs choose prime ministers, and prime ministers choose and work for them.

“They’ve got to be accountable to the electorate, and Boris is accountable to the electorate – Lord Geidt is not.”

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Mr Johnson has argued that he “cannot and would not wish” to give up his power as the ultimate arbiter on ministerial rules.

“That vital responsibility is quite properly mine alone and, as an elected politician, one for which I am ultimately accountable to the electorate,” he said in a letter to chairman of the Committee on Standards in Public Life Lord Evans.

Lord Geidt’s review is among a number of inquiries currently under way into the funding of the refurbishment of the prime minister’s apartment, which has sparked sleaze claims.

The PM has insisted the row over refurbishments to the flat is a “farrago of nonsense” and “I don’t think there’s anything to see here”.

A fresh poll ahead of the 6 May elections suggests the controversy has had little immediate effect on public support for the Conservatives.

The YouGov poll on Westminster voting intention carried out on Tuesday and Wednesday put the Tories on 44%, unchanged from a week earlier. Labour was down a point on 33%.

Along with the flat controversy, Mr Johnson faced further embarrassment as it emerged his mobile phone number had been openly available online for 15 years.

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