Prime Minister Rishi Sunak has defended himself after the MP embroiled in the Westminster honeytrap sexting scandal quit the Conservative Party voluntarily, rather than being kicked out.

William Wragg announced his decision on Tuesday, a day after he resigned as vice-chairman of the Tory 1922 committee and chair of the Commons’ public administration and constitutional affairs committee.

It followed his admission in The Times that he had given some of his colleagues’ phone numbers to someone he met on a dating app.

The MP for Hazel Grove in Greater Manchester, who will now sit in parliament as an independent, garnered the support of some MPs and ministers following his apology in the newspaper, where he said the person had “compromising things” on him and he was “scared”.

But others reacted with fury and called on Mr Sunak to withdraw the whip from him.

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Now that Mr Wragg has acted first, the prime minister has come in for criticism, with a senior Tory telling Sky News: “Rishi is so weak Wragg decided he’d have to fire himself instead.”

Labour joined in on the attack, with the party’s national campaign coordinator Pat McFadden saying it was “another indictment of Rishi Sunak’s weakness”, adding the prime minister “puts party management first every time – and he can’t even do that properly, it is no way to run a country”.

But Mr Sunak appeared to claim he wanted to leave the police to carry out their investigation before he took any action against the MP.

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The prime minister told LBC: “[Mr Wragg] has spoken about it very clearly, he has apologised for what happened, taken responsibility for it.

“There is a police investigation happening, it is important that we work through these things in due time… the important thing here is we let the police investigations run their course and also that it is a reminder about the importance, particularly people in public life, that they take care with unsolicited messages.”

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Pushed over whether it was a sign of weakness not to remove the whip, Mr Sunak added: “Well people can judge me if they want to judge me on that, that’s fine, I accept that.”

Scotland Yard has said it is investigating reports of the so-called “honeytrap” scam after it was suggested at least 12 men in political circles received unsolicited messages, raising security concerns.

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