John Caudwell said: "Sort it out, Boris, or step aside and let someone else sort it out so that the Tories aren't wiped out at the next election."

The Phones4U founder donated £500,000 to the Conservatives ahead of the 2019 general election.

He criticised the government's perceived "arrogance and hypocrisy".

Mr Caudwell was one of the Conservative Party's biggest individual donors at the last general election, and has previously given money to pro-Brexit Tory MP Sir Bill Cash.

He told BBC News: "Although I have always obeyed the rules I have never been puritanical about lockdown restrictions so I find it difficult to personally get excited about an outdoor drinks party. But it's the perceived arrogance, hypocrisy and rule breaking that is impossible to justify.

"While the rest of us were striving to follow the ever-changing rules - including myself, even when I deemed them to be excessive at best, nonsensical at worst - those who were setting those rules were, apparently freely and frequently, disregarding them.

"Each one of these new revelations gives greater force to the accusation that areas of the government think it's 'one rule for them, one rule for the rest of us'.

"This is disastrous."

'Socially distanced drinks'

He added that he was not a "dyed-in-the-wool Tory" and had been critical of the government's economic recovery plans, urging more investment in apprenticeships and renewable energy.

But he added: "I do think the Conservatives are the best party to govern this country, particularly as we look to navigate opportunities post-Brexit.

"Sort it out, Boris, or step aside and let someone else sort it out so that the Tories aren't wiped out at the next election."

Alasdair Locke, who has donated £280,000 to the Conservative Party since Mr Johnson came to power, said the lockdown parties were "something the media is making a great deal of" and voters would be concerned with "serious stuff" at the next election.

"I really don't think a leadership change, or challenge, is needed at this stage. A bit more grip would help but that will probably come."

The prime minister is under growing pressure from Labour - and anger from some Conservatives - over his alleged attendance at a previously unreported Downing Street party.

It comes after ITV published a leaked email from the PM's principal private secretary, Martin Reynolds, inviting 100 staff to "socially distanced drinks in the No 10 garden" on 20 May 2020.

The invitation for the event, which was organised when strict lockdown rules were still in place, encouraged people to "bring your own booze" and "make the most of the lovely weather".

Witnesses told the BBC the PM and his wife had been among about 30 people who attended the gathering.

But Mr Johnson has declined to say whether he was one of them.

The PM's official spokesman also refused to comment on the claims while the investigation was taking place, but he added that the prime minister retained full confidence in Mr Reynolds.

Senior civil servant Sue Gray is investigating lockdown parties in Downing Street, including the event on 20 May 2020, and is expected to report shortly.