A senior member of the 1922 Committee and a Scottish Conservative MP said they would be discussing with colleagues how to tackle the electoral problem that Mr Johnson has become in the wake of two disastrous by-election results confirmed on Friday.
And former Conservative leader Michael Howard urged the Prime Minister to quit for the good of their party and the nation, as he urged the Cabinet to consider resigning to force him out.
"The party, and even more importantly the country, would now be better off under new leadership. Members of the Cabinet should very carefully consider their positions," he said.
The Prime Minister will return from Rwanda, where he has been attending the Commonwealth Heads of Government Meeting, to face an ever- increasing number of demands to resign.
In Wakefield, the Conservatives meekly handed back control of a ‘red wall’ seat taken in 2019 to Labour.
Meanwhile, in Tiverton and Honiton, the Liberal Democrats overturned a 24,000-vote majority with a 30 per cent swing to take a seat that will send shivers down the spines of senior Tory MPs in even the safest of seats.
The result is the third biggest swing from the Conservatives to Liberal Democrats and the 12th biggest swing in history.
Mr Johnson was further damaged and weakened when co-chairman of the Conservative Party and Cabinet minister, Oliver Dowden, resigned from the government.
In his resignation letter, the former culture secretary said the by-election results were the “latest in a run of very poor results for our party”.
He said: “We cannot carry on with business as usual. Somebody must take responsibility and I have concluded that, in these circumstances, it would not be right for me to remain in office.”
Nicola Sturgeon labelled the results a “monumental, massive, humiliating vote of no confidence” for the Prime Minister.
Mr Dowden’s language was later echoed by a spokesperson for the Scottish Conservatives.
The spokesperson said: “It's always disappointing to see the Conservative party lose seats, especially a formerly safe seat where a huge majority has been overturned. The scale of these losses speak for themselves.
“As Oliver Dowden has said this morning, we cannot continue with ‘business as usual’. We need to listen to the public as a party and reflect on these votes.”
Scottish Tory MP Andrew Bowie said he would vote against the Prime Minister again if given the opportunity, but claimed the UK needed to focus on the “big issues”.
“I do believe that we shouldn’t be naval gazing and worrying about who is the current leader and we do need to be focusing on the big issues facing the country, such as the cost-of-living situation and supporting the government of Ukraine,” he told the BBC’s Good Morning Scotland.
“But no, I don’t think we can carry on as if it’s business as usual.”
When asked what MPs should do about their lack of faith in Mr Johnson, Mr Bowie replied: “I think that is for others to be discussing this morning.”
However, the Scottish Tory MP said voters had made their opinions clear in the by-elections, and stressed many MPs and party members would now be “discussing amongst ourselves how we move forward”.
Mark Diffley, a pollster and researcher, said the Scottish Conservatives were in desperate need of a resolution to what he labelled the “Johnson problem”.
He said: “The Tories up here, what they need is a resolution to the Johnson problem.
"The resolution that they [Scottish Conservatives] would clearly want as evident by how most of them voted in the recent confidence vote is for him to go and the sooner the better.
"That’s when I think they can rebuild.
"It’s hard to draw any other conclusion than the fact the Prime Minister is a drag on support for the Tories in Scotland and it is very, very difficult for them to go out and campaign and canvas on behalf of a Prime Minister whom most of them want to get rid of.”
Conservative support in Scotland has been slowly declining despite a strong result at the 2021 Holyrood election.
The party, led by Douglas Ross, has lost second place in the polls to Scottish Labour and is languishing in the high teens in some polls, with Mr Johnson often cited as the most unpopular politician among Scots.
Mr Diffley said while Labour was making gains in Scotland, particularly in the Westminster voting intentions, this was at the expense of a weakened Tory party rather than eating into the SNP dominance.
He also warned the gains, which have seen Labour gain second place and sitting in the low to mid 20s in terms of voting percentage, could easily be reversed in the coming year.
The pollster said: “If a much more palatable Prime Minister from Douglas Ross’s point of view comes into place and it looks like we are heading towards another referendum and we get that hardening of unionist attitudes towards independence, you can quite easily see how the relatively modest gains Labour in Scotland has made in the last year or so could be completely wiped out by a mini Scottish Tory revival.
"Poll after poll after poll and election after election shows nothing really changing in terms of the pre-eminence of the SNP at the moment.
"It doesn’t feel like the earthquake is anywhere near happening in Scotland, like particularly the Devon result suggests is happening in England.”
Despite this, the by-election results have buoyed Labour, with one senior figure stating they had effectively “fired the starting gun of the next Labour government”.
The result in Wakefield, a swing of 12.7 per cent in favour of Labour, sparked several commentators to highlight that a nationwide repetition of that swing would not be good enough for Labour to comfortably win an outright majority.
However, key members within the party told The Scotsman the by-election result had bettered their own expectations and placed Labour as the biggest party at a general election.
They argued around 290 Labour MPs and a strong Liberal Democrat showing would be enough to keep the Conservatives out, with Labour as the biggest party.
One Labour source said: "What the two by-elections have done is they’ve essentially fired the starting gun on the next Labour government because the Liberal Democrats are not going to be in government, but they might just win enough seats to make a difference.”
The source added: “Scots can now see that Labour can win and therefore Scottish voters are going to have to make the choice of whether they are going to vote for the SNP opposition or a Labour government.
"That’s going to be hugely powerful.”
The threat of the SNP working with Labour in the House of Commons has been used by the Conservatives for several years as a way of bolstering their own unionist credentials.
However, the Labour source said a strong Liberal Democrat party would allow the Labour party to demonstrate how it could be in government without relying on the support of the SNP.
"With the Liberal Democrats looking as if they can do quite well, it neutralises much more so the threat of the nationalists being in government,” they said.
Senior figures within the Conservative party spent Friday calling for the Prime Minister to consider his position, while members of Mr Johnson’s Cabinet continued to voice support.
Chancellor Rishi Sunak said he was “sad” to see the resignation of Mr Dowden, the former culture secretary, but said “we all take responsibility for the results”.
But former Tory leader Michael Howard said a leadership campaign to replace Mr Johnson was urgent, not only electorally, but “for the good of the country”.
He said the Tories’ double by-election defeats made clear Mr Johnson no longer had the ability to win votes.
Asked whether the Prime Minister should stay in post, Mr Howard told BBC Radio 4’s World at One programme: “I’m afraid I’ve very reluctantly come to the conclusion that he shouldn’t.”
He added: “I think members of the Cabinet should very carefully consider their positions as Oliver Dowden has done, and it may be necessary for the executive of the 1922 Committee to meet and to decide to change the rules so that another leadership election could take place.
“Those are the two things which I think could make a difference. But we shall have to see whether either of them comes about.”
Asked if in his eyes, electorally, it was that urgent, Mr Howard said: “I think it is not only electorally, but for the good of the country. I think the country needs new leadership. And I think the time has now come to provide it.”
Sir Geoffrey Clifton-Brown, the treasurer of the influential backbench 1922 Committee, said he would discuss the by-election defeats at a Conservative annual general meeting on Friday evening and expected to make “difficult decisions”.
The 1922 Committee has the power to change the rules around no confidence votes – something the body threatened former prime minister Theresa May with prior to her resignation.
The MP for The Cotswolds told the BBC’s Today programme that MPs would in coming days decide whether steps should be taken to oust Mr Johnson.
Speaking on a phone line, Mr Clifton-Brown said: “I’m not going to come on out this morning and speculate on behalf of my colleagues as to whether we should or shouldn’t change the rules. Clearly what’s going to happen over the next few days is the Prime Minister is going to set out to both his Cabinet and with us as Members of Parliament.”
The line then broke off momentarily, before he added: “We will then in the parliamentary party have to make a judgment as to whether we think that is a satisfactory explanation or whether we should actually take steps to have a new Prime Minister.”