Boris Johnson and former finance minister Rishi Sunak were leading the potential contenders to replace British Prime Minister Liz Truss on Friday, with candidates canvassing support to become Conservative Party leader in a fast-tracked contest.

After Truss quit on Thursday, ending her six weeks in power, those who want to replace her were trying to find the 100 votes from Conservative lawmakers needed to run in a contest which the party hopes will reset its ailing fortunes.

With the Conservatives all but facing a wipeout in the next national election according to opinion polls, the race is on to become the fifth British premier in six years.

The winner will be announced on either Monday or Friday next week.

In what would be an extraordinary comeback, Johnson, who was ousted by lawmakers just over three months ago, was running high up the ranks alongside Sunak to be crowned the next prime minister.

"I think he's got that proven track record to turn around things. He can turn it around again. And I'm sure my colleagues hear that message loud and clear," Conservative lawmaker Paul Bristow said of Johnson on LBC radio.

"Boris Johnson is the character the Labour Party fears, Boris Johnson can win the next general election," he said.

Johnson, who left office comparing himself to a Roman dictator brought into power twice to fend off crises, might face difficulty in reaching the 100 votes after his three-year tenure was blighted by scandals and allegations of misconduct.

One of his former advisers, who no longer speaks to Johnson and requested not to be identified, said he was unlikely to reach the target, having alienated dozens of Conservatives during his scandal-ridden tenure.

But Will Walden, who also worked for Johnson, told Sky News the former prime minister was returning from holiday and was taking soundings.

The contest began on Thursday, just hours after Truss stood in front of her Downing Street office to say she could not go on.

Sunak, the former Goldman Sachs analyst who became finance minister just as the COVID-19 pandemic arrived in Europe, is favourite with bookmakers, followed by Johnson. Running in third is Penny Mordaunt, a former defence minister popular with Conservative Party members.

None have formally declared their candidacy.

Truss quits

Truss quit on Thursday after the shortest, most chaotic tenure of any British prime minister after her economic programme shattered the country's reputation for financial stability and left many people poorer.

Truss said she could no longer carry out her programme after her economic plan roiled markets and ended up on the cutting room floor when she was forced to bring in a new finance minister.

"I have therefore spoken to His Majesty the King to notify him that I am resigning as leader of the Conservative Party," said Truss, who was supported only by her husband with her aides and loyal ministers noticeably absent.

The sight of yet another unpopular prime minister making a resignation speech in Downing Street – and the start of a new leadership race – underscores just how volatile British politics has become since the 2016 vote to leave the European Union.

Some Conservative lawmakers hope the race to replace her will be quick and simple, urging the hopefuls to coalesce around one candidate to reduce the pain of another bruising contest.

Sunak, proven right in his warnings that Truss's fiscal plan threatened the economy, is the favourite but remains deeply unpopular with some Conservatives after he helped to trigger the summer rebellion against Johnson.

Mordaunt is seen as a fresh pair of hands largely untainted by earlier administrations. But she is also untested and, so far, she is lagging Sunak and Johnson in getting backers.

Whoever takes over the party, they have a mountain to climb to try to restore or renew the reputation of the Conservative Party, which holds a big majority in parliament and need not call a nationwide election for another two years.

"Whether or not a change of leader is going to be sufficient to make the Conservatives actually electorally credible is certainly highly debatable," political scientist John Curtice told LBC.

"The problem for the Conservatives is that the brand of them as a party that can mind the economy... has now been very, very badly tarnished, and it may be very difficult to recover within the space of two years."