The contest to replace British Prime Minister Boris Johnson gathered pace on Sunday as five more candidates declared their intention to run, with many pledging lower taxes and a clean start from Johnson's scandal-ridden premiership.

Johnson on Thursday said he would resign as prime minister, after many of his lawmakers and cabinet colleagues rebelled over his handling of a series of scandals, including breaches of lockdown rules in gatherings at his Downing Street office.

Junior trade minister Penny Mordaunt officially declared she was running on Sunday, joining transport Secretary Grant Shapps, finance minister Nadhim Zahawi and former ministers Jeremy Hunt and Sajid Javid, who announced their candidacies for the leadership in time for the Sunday newspapers, taking the total to nine.

"This is a critical inflection point for our country. I believe that a socialist or socialist-led coalition government at the next election would be a disaster for the UK," Mordaunt said in a statement. "We must win the next election."

The Conservative Party's 1922 Committee of legislators, which groups all backbench members of parliament, will set out the exact rules and timetable for the contest in the coming days, and is looking to speed up the process of whittling down the contenders to a final two.

Conservative Party members would then have the opportunity to vote on the two who reach the run-off, with a result expected by the Conservative Party conference in October, and maybe earlier.

Entering the race, Shapps, Zahawi, Hunt and Javid all pledged tax cuts, setting them against current favourite, former finance minister Rishi Sunak, whose budget last year put Britain on course for its biggest tax burden since the 1950s.

"I believe in a lower tax, lower regulation, cut-the-red-tape economy," Shapps told Sky News, adding he would hold an emergency budget to bring forward a one pence reduction in the income tax rate, currently planned in 2024, and look to reduce the size of the civil service.

"I also want to stop, or freeze if you like, the proposed increase in corporation tax ... and (make) sure we cut the cost of the state," he added.

Hunt, a former foreign minister who came second in the leadership contest in 2019 when Johnson came to office, and Javid, who twice resigned from Johnson's government, both said they would cut corporation tax to 15 per cent.

Hunt said that no Conservative should either raise taxes or offer unfunded tax cuts. Asked if cutting taxes would lead to inflation, Hunt said: "I don't agree with that when it comes to business taxes."

"If you stimulate consumer demand, when there's some demand-led inflation, there is that risk, but we must bear down on inflation. That's why I'd be very careful not to promise (tax) cuts that would stoke inflation," he said.

The Mail on Sunday said Foreign Secretary Liz Truss would launch her campaign on Monday with a promise to cut taxes and tackle the cost-of-living crisis, while one of her main rivals for the role, Defence Secretary Ben Wallace, has ruled himself out.