Boris Johnson has claimed there isn’t “anything to see here” as he fights inquiries into who paid for his Downing Street flat renovations, as a new poll showed the Tories’ lead undented despite the growing questions.

The prime minister, who currently faces three probes, 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.

On Thursday, the prime minister also said he would comply with another investigation, by the Electoral Commission, into whether any transactions related to the works were properly reported.

“We will comply with whatever they want. I don’t think there’s anything to see here, or to worry about, but what we are doing is focusing on the stuff that really matters,” he said.

It comes as the parliamentary commissioner for standards, Kathryn Stone, said she would announce in the week of 10 May the names of any MPs she is investigating.

It is not known if Mr Johnson is also being investigated by Ms Stone, but there are rumours she may also be doing so. If she is, that would mean he is subject to four inquiries.

Despite a week in which the PM’s activities have been closely scrutinised, a YouGov poll on Westminster voting intention carried out on Tuesday and Wednesday – well into the row over who paid for what – put the Conservatives on 44%, unchanged from a week earlier. Labour was down a point on 33%.

Mr Johnson’s attempts to claim there in nothing “to see” have been unable to quell accusations that he has done something wrong.

Former attorney general and Tory MP Dominic Grieve told Sky News Mr Johnson was trying to brush off questions for a reason.

He said: “He plainly thinks there is something which is embarrassing to him. And it’s disgraceful that a prime minister of the United Kingdom should be playing games like this.

“One has to assume from it that there is something disreputable. The evidence that has emerged suggests that he has been dishonest and has lied about where he got the money to refurbish his apartment.

“He appears on the face of it to be in considerable trouble. I think it does matter.”

Christopher Geidt, the Queen’s former private secretary, was appointed on Wednesday and launched a separate 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.”

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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 leader Sir Keir Starmer said he thought the issue of who paid for the refurb “is getting a bit farcical”.

He said: “I think the prime minister could deal with this very quickly – all he’s got to do is answer a simple question, which is: Who paid initially for the redecorating of his flat?”

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In Lord Evans’ reply to Mr Johnson, he welcomed the appointment of Lord Geidt but expressed concern that the new adviser is not allowed to investigate with full independence, as was recommended by his committee.

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

The PM 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”.

Mr Johnson told reporters on Thursday there was “absolutely nothing” wrong with John Lewis and the one thing he “objects to in this whole farrago of nonsense is that anything – I love John Lewis”.

The taxpayer funds a £30,000 annual allowance but the revamp of the four-bedroom flat, which reportedly involves the company Soane, co-founded by top interior designer Lulu Lytle – whose fans include Prince Charles and Lord Cholmondeley – has reportedly stretched beyond that.

Vaccines minister Nadhim Zahawi told Sky News the government has reformed Lord Geidt’s role to allow him to be “proactive rather than reactive” and the PM will “absolutely make sure” he delivers everything asked of him.

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

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 funded it and he paid them back.

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