In an extraordinary intervention, the former prime minister said it would be ‘unwise and may be unsustainable’ for Mr Johnson to remain in office while a new Tory leader is elected.
It came as Labour leader Sir Keir Starmer vowed to table a Commons no-confidence motion in the Prime Minister unless he hands the keys to No 10 to a caretaker leader.
Mr Johnson yesterday fought to stay in Downing Street until October and began rebuilding his Cabinet as the battle to replace him got under way.
Constitutional experts are clear he is entitled to remain in No 10 until a new party leader, who will be able to form a government, is in place.
Sir Keir Starmer, pictured with his wife, Lady Victoria, visiting Wimbledon yesterday, is planning to force a vote of no confidence in Prime Minister Boris Johnson as early as next week
Boris Johnson, pictured, said he plans to remain as PM until the party announces a new leader in the autumn
Former Tory PM John Major, pictured, said Johnson should leave Downing Street immediately
Sir Keir Starmer took a break from the drama unfolding at Westminster yesterday and headed to Wimbledon
But Sir John warned the new Cabinet would not be able to ‘restrain him’. In a letter to Sir Graham Brady, chairman of the Tory backbench 1922 committee, he suggested Deputy Prime Minister Dominic Raab could be installed as acting premier until the next leader is chosen. Sir John also said as an alternative there could be a shorter leadership contest, with MPs electing the leader and grassroots Tory members to endorse the result.
Meanwhile Sir Keir, who yesterday went to Wimbledon and sat in the royal box with his wife Victoria, called for a general election and threatened to try to oust Mr Johnson if he refuses to hand over to a caretaker.
He said: ‘If they don’t get rid of him then Labour will step up, in the national interest, and bring a vote of no confidence because we can’t go on with this Prime Minister clinging on for months and months to come.’
Tory MPs turned on Sir John, branding his proposal ‘not very democratic’ and ‘wrong’.Michael Fabricant told BBC News: ‘It’s quite interesting isn’t it that John Major has come up with a proposal that maybe the rules should be changed and it should be the MPs who choose the successor. I’m not sure I would go with it as it’s not very democratic to not involve the Conservative Party as a whole.’
Mark Pritchard, former chairman of the 1922 committee, said he disagreed with Sir John.
He told Sky News: ‘I think on this one he’s got it wrong. There’s a precedent. David Cameron in the transition carried on as Prime Minister, albeit for just a few weeks – Theresa May for six, seven weeks.
The Labour leader was spotted enjoying the posh seats in Centre Court’s Royal Box, alongside his wife Victoria, on women’s semi-finals day
Sir Keir’s journey from SW1A to SW19 came shortly after he unveiled a plot to remove Boris Johnson from power immediately
The Labour leader and his spouse watched Tunisia’s Ons Jabeur reach the women’s final after she defeated Germany’s Tatjana Maria
Sir Keir shared a joke with TV presenter and Liberal Democrat peer Floella Benjamin
‘I think it’s right that the Prime Minister should carry on. He’s set out a timetable; he’s said he’s going to go. I think people should leave him alone and allow him to get on and govern the country for the next few months.’
Veteran Tory MP David Davis cautioned against replacing Mr Johnson too quickly.
‘My concern is to pick the most straightforward way through this change we have to do and every way we pick has got problems. But the one of waiting until you have got a new leader provides the least problems,’ he told BBC Radio 4’s Today.
Prior to resigning Mr Johnson had reshuffled his Cabinet after the avalanche of resignations.
Greg Clark was appointed Levelling Up Secretary. James Cleverly was made Education Secretary and Kit Malthouse appointed as new Chancellor of the Duchy of Lancaster.
Will Quince also made a surprise return as education minister, despite resigning on Wednesday. Johnny Mercer was given his old role of veterans’ minister, which he quit last year.
The Prime Minister, who has seen vast swathes of Tory MPs turn against him over the past 48 hours, this afternoon announced his intention to leave Downing Street
But Mr Johnson also revealed how he wants to stay in office until a new Tory leader is elected, which could take a number of weeks, if not months
Many Conservatives’ are resisting the PM’s plan – wanting him to go as soon as possible – and Sir Keir had earlier attempted to further fuel the Tory civil war
He vowed to table a vote of no confidence in Mr Johnson and the Government in the House of Commons, if the PM was not removed immediately