Boris Johnson has been backed by one of his ministers to “face down” a test of his leadership as the Conservative Party braces for a confidence vote.

Business minister Paul Scully said the Conservative Party “may well have a vote of confidence” in Mr Johnson following backlash from backbench MPs in the wake of the so-called partygate affair.

But the frontbencher said he believed the Prime Minister would “win that” contest.

It comes as The Sunday Times reported that the threshold for a leadership contest might have already been reached.

Under Conservative Party rules, if 54 letters from MPs are submitted to Sir Graham Brady, the chairman of the 1922 Committee of backbench Tories, asking for a leadership poll then a vote is called.

The Sunday Times said it had been told as many as 67 letters had gone in, paving the way for Sir Graham to potentially announce a secret ballot among MPs as soon as Monday.

The newspaper said the vote to decide if Mr Johnson remains leader could then take place on Wednesday.

Transport Secretary Grant Shapps told the BBC on Sunday morning that he did not think the Prime Minister would face a confidence test.

However, Mr Scully’s comments to Channel 4’s The Andrew Neil Show hours later suggests his supporters may have accepted that the rebels have the numbers they need to spark a vote on his future.

Mr Scully said: “We may well have a vote of confidence.

“If it does happen, the Prime Minister, I know, will face it down.”

According to PoliticsHome website, a briefing document is being circulated among Tory MPs warning that the party is on course to lose the next election due to the damage done to its reputation after revelations about raucous No 10 parties held during lockdown.

The document being shared online states: “The only way to end this misery, earn a hearing from the British public, and restore Conservative fortunes to a point where we can win the next general election, is to remove Boris Johnson as prime minister.”

A veteran Labour MP called the alleged coup-urging document “devastating”.

Chris Bryant tweeted: “Whether or not it is genuinely from Tory rebels, this is what we in Labour will be saying up until the election unless the Tories unseat Boris Johnson.

“The only conclusion for a sane Tory must be to remove him now.”

Tory election fears will have been fuelled further by polling carried out ahead of the Wakefield by-election by JL Partners.

The survey found the Conservatives could lose the key battleground seat, one of tens of constituencies Mr Johnson took from Labour in the so-called Red Wall during the 2019 general election, by as much as 20 points to Sir Keir Starmer’s party this month.

James Johnson, co-founder of JL Partners and a former Downing Street pollster during Theresa May’s tenure, tweeted that the results indicated that “partygate has crystallised historic concerns about the Tories and turned the people of Wakefield decidedly against them”.

With the Tiverton and Honiton by-election due to be held on the same day as Wakefield, on June 23, Mr Johnson faces the prospect of losing seats to Labour in the North of England and the Liberal Democrats in the South West.

The by-elections are being held in controversial circumstances, with Tiverton and Honiton vacated by Neil Parish after he admitted to twice watching pornography in the Commons, while former Wakefield incumbent Imran Ahmad Khan quit after being being found guilty of sexually assaulting a boy.

Mr Shapps, when asked about the poll findings on BBC’s Sunday Morning programme, argued it was “best to allow the people to speak” before judging the party’s performance.

Tory popularity has sunk in recent months following reports and later confirmation of coronavirus rule-breaches at the top of Government.

Last month, an investigation published by senior civil servant Sue Gray laid bare the details, finding that raucous parties had taken place, with staff throwing up, getting into altercations and being rude to security staff.

The Prime Minister was found to have attended a number of leaving dos for aides, giving speeches and joining in the drinking of alcohol, despite him at the same time telling the public not to see sick and dying loved ones in a bid to stop the spread of the virus.

The Metropolitan Police handed Mr Johnson a fixed-penalty notice for his part in attending his own birthday bash in Downing Street in June 2020 when indoor mixing was banned.

With Scotland Yard and Ms Gray’s inquiries concluded, Mr Johnson now faces a parliamentary investigation over whether he misled MPs with his reassurances that Covid regulations were followed by his staff in No 10.

Mr Scully, who is also minister for London, told Channel 4 he did not believe that his leader had “wilfully misled parliament” but voiced frustration at “the way that we as a Government have handled this issue.”

He added: “It should have been actually dealt with before Christmas. That was one of the things I regret, that it has stretched out for so long.”