Boris Johnson has said he will have the final say on any investigation into ministerial misconduct after appointing an independent adviser to look at how his Downing Street flat refurbishment was paid for.

Christopher Geidt, the Queen’s former private secretary, was appointed on Wednesday and launched an investigation straight away, but questions have been asked about what powers he will actually have.

In a letter to Lord Evans, the head of the committee on standards in public life, Mr Johnson confirmed that he would remain the ultimate arbitrator of whether a matter should be investigated – not the independent adviser.

Mr Johnson wrote: “The constitutional position of the prime minister, as having sole responsibility for the overall organisation of the executive and recommending the appointment of ministers, means that I cannot and would not wish to abrogate the ultimate responsibility for deciding on an investigation into allegations concerning ministerial misconduct.

“That vital responsibility is quite properly mine alone and, as an elected politician, one for which I am ultimately accountable to the electorate.”

He added that he believes it is “necessary to avoid creating incentives” for the independent adviser to investigate “trivial or vexatious complaints”.

Vaccines minister Nadhim Zahawi told Sky News the government has reformed Lord Geidt’s role to allow him to be “proactive rather than reactive”.

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He added: “The prime minister will absolutely make sure that he delivers everything that Lord Geidt asks for to be able to conduct that investigation.

“The prime minister has been very clear that he paid for this, that he also followed all the ministerial code, he took advice and if Lord Geidt, in his investigation, requires the prime minister to make any other declarations, then he will also do that.”

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Need to know if PM ‘in hock to funder’

The Labour Party has called for Lord Geidt to be given powers to trigger investigations into ministers himself, but Mr Johnson’s letter to Lord Evans makes it clear he will not allow that.

Labour MP Liz Kendall said Lord Geidt was not a “properly independent adviser with the ability to initiate investigations”.

She told Sky News: “They’re saying he can suggest investigations, that’s not the same as saying ‘you have a right to initiate investigations’.

“The whole reason the last person quit was because Boris Johnson refused to accept the findings, so I’m afraid the PM has form here.”

She said it matters that the public knows who initially paid for the flat refurbishment because “you have to have confidence you know who’s funding people so you can see if there’s any conflicts of interest”.

Mr Johnson has repeatedly said he paid for the refurbishment but has refused to answer whether he paid for the initial cost or whether a donor or the Conservative Party paid it and he paid them back.

Ms Kendall added: “If there has been a loan and that person is looked on favourably the risk is the prime minister could make a decision that favours that donor.”

Mr Johnson has insisted he has not broken any laws or rules over renovations of his Number 11 residence.

The Electoral Commission announced on Wednesday it is also looking into whether any transactions related to the works on the prime minister’s flat – above 11 Downing Street – were properly reported.

They said there were “reasonable grounds to suspect that an offence or offences may have occurred”.

Mr Johnson and his fiancée, Carrie Symonds, are said to have wanted an overhaul of the flat in order to replace what has been termed Theresa May’s “John Lewis furniture nightmare”.

They used top interior designer Lulu Lytle – whose fans include Prince Charles and Lord Cholmondeley – to revamp the four-bedroom flat.