• U.K. Prime Minister Boris Johnson's leadership is hanging by a thread.
• At least 38 ministers and aides have quit his government in the last 24 hours.
• British Finance Minister Rishi Sunak and Health Secretary Sajid Javid both resigned on Tuesday in protest against Johnson's leadership.
• But despite calls to resign, the prime minister shows no signs of being ready to stand down.

LONDON — U.K. Prime Minister Boris Johnson on Wednesday vowed to remain in 10 Downing Street despite growing calls for him to resign and at least 38 ministers and aides quitting his government in the last 24 hours.

Johnson reportedly said that he is remaining "absolutely defiant" and "does not intend to resign," according to Sky News, despite some of his most loyal ministers telling him to step down on Wednesday evening.

Interior Secretary Priti Patel is said to be the latest in a growing list of close allies of Johnson that has called on the prime minister to step down.

Speaking earlier in the House of Commons, Johnson said he secured a "colossal mandate" from the British electorate in 2019 and vowed to "keep going."

The political saga in Britain gathered pace on Tuesday night after the shock resignations of two of his most high-profile ministers. British Finance Minister Rishi Sunak resigned Tuesday evening, saying the government should be run "properly, competently and seriously." Health Secretary Sajid Javid, likewise, resigned in protest against Johnson's leadership, which has been beset by controversy and scandal in recent months.

Several ministers have defended Johnson, however, expressing their loyalty to him. Top figures staying in the Cabinet include Deputy Prime Minister Dominic Raab and Foreign Secretary Liz Truss.

Odds of a snap election

For now at least, the loyalty of a few top ministers diminishes the immediate prospect of a snap election in Britain. For that to happen, Johnson would have to resign or face another confidence vote.

As he faced such a vote only last month, a new challenge would require a rule change to allow another vote within the next 12 months. Reports on Wednesday suggested that that rule change could come as earlier as next week.

"Current party rules stipulate that Johnson cannot face another no-confidence vote until next summer. But the main risk now is either that those rules will be changed to force another vote, or Johnson is pressured to voluntarily step down," Allan Monks, an economist at JPMorgan, said in a note Tuesday night.

"Events could move very quickly, with a Conservative leadership contest potentially putting in place a new Prime Minister in the next couple of months or so – ahead of the party's annual conference in early October."

Market response

Sterling was trading at a two-year low against the dollar on Wednesday as the U.K.'s political instability played out. How markets react in the next few days will be closely watched.

"There's paralysis and there's so much uncertainty over how it will exactly play out," Ben Emons, managing director of global macro strategy at Medley Global Advisors, told CNBC on Wednesday.

"The way the markets responded, somewhat negatively as sterling and U.K. [government bond] yields fell, but then they recovered and I think that does indicate that as much as there's uncertainty surrounding the Cabinet and Johnson's position, it has not fallen apart, he does still have support," he said.

"We're not going to see any snap election, they have to elect a new leader for that to happen, so I think the markets take some comfort in [the fact that] we're going to enter a period of some uncertainty but that uncertainty reflects the status quo, nothing will change in the economy or with policy," he told CNBC's "Squawk Box Europe."

String of scandals

The latest political upheaval to hit the U.K. comes after a series of controversies, ranging from the "partygate" scandal with Johnson and multiple other government officials who were found to have broken Covid pandemic lockdown rules, to sleaze allegations — the latest of which involves Chris Pincher, the Conservative Party's former deputy chief whip, responsible for maintaining party discipline.

Pincher resigned and was suspended as a Conservative Party MP last week, following accusations that he drunkenly groped two men at a private members' club. It has since emerged that Johnson appointed him to the role despite knowing of previous misconduct allegations against him.

Johnson apologized for appointing Pincher as deputy chief whip, but it was too little, too late with the high-profile resignations coming just minutes after.

Johnson has survived a number of challenges to his leadership in recent months, as well as calls for him to resign, particularly following a bruising confidence vote and the Conservative Party's loss of two key by-elections in the last month as the British public's faith in its leader wears thin.

A snap YouGov poll conducted Tuesday found that 69% of Britons surveyed want Johnson to resign. The poll of 3,009 adults found that only 18% want him to stay on.

Among the Conservative voters polled, 54% said they want to see Johnson go, while 33% want him to stay on, showing that Johnson has become an unpopular figure for many voters initially attracted to his leadership in 2019, when he won a massive 80-seat majority on his election bid to "get Brexit done."

Britain's opposition Labour Party leader, Keir Starmer, tweeted Tuesday that "the Tory party is corrupted and changing one man won't fix that. Only a real change of government can give Britain the fresh start it needs."

Nadhim Zahawi, Britain's new finance minister, told Sky News on Wednesday that he backed the prime minister and said "the team in government today is the team that will deliver." However, there were reports on Wednesday evening that even the brand new finance minister had joined the chorus of people telling Johnson to go.

Ed Davey, leader of the opposition Liberal Democrats, told CNBC Wednesday morning that "it's clearly in the national interest for Boris Johnson to go" and that Johnson had been proven to be deceitful in the past.

"Having someone as a British prime minister who clearly doesn't tell the truth and who lies on an industrial scale, is damaging to our democracy, it's damaging to Britain's reputation around the world and it's damaging for our investment. ... We need a government that knows what it's doing," he said.

Johnson has been accused of lying on multiple occasions during his time in office though he has invariably denied doing so, and has denied misleading Parliament over the partygate scandal, over which there is an ongoing inquiry.