The race to replace Boris Johnson as Conservative leader and Britain's prime minister is down to five candidates after the second round of voting among Tory MPs on Thursday.

While former finance minister Rishi Sunak is leading the way with his MP colleagues, second-placed Penny Mordaunt is polling out front with party members, who will ultimately decide the winner.

The UK's first Hindu finance minister, and Britain's richest MP, Sunak quit last week and declared he was standing three days later.

Rishi Sunak quit as finance minister last week
Rishi Sunak quit as finance minister last week AFP / Daniel LEAL

Sunak, 42, launched his campaign on Tuesday, saying he would not "demonise" the outgoing Johnson despite helping to trigger his demise.

His star rose rapidly during his early stint as finance minister, overseeing the furlough scheme that subsidised workers during the coronavirus pandemic.

He has long been seen as Johnson's most likely successor, but his popularity has plunged recently amid rampant inflation and questions over his private wealth and family's tax arrangements.

Sunak, who supported Brexit during the 2016 referendum, earned millions in finance before politics, and his Indian wife Akshata Murty's father co-founded the IT giant Infosys.

Penny Mordaunt was the first woman to be UK defence secretary
Penny Mordaunt was the first woman to be UK defence secretary AFP / ISABEL INFANTES

His apparent reluctance to embrace immediate tax cuts could also harm his prospects, while recent polls among members have also shown him trailing most of the leading competitors.

Mordaunt, 49, is currently the favourite to win the whole contest based on her perceived popularity with the party's grassroots.

Several recent polls have shown her beating all other contenders in the final run-off put to members.

Foreign Secretary Liz Truss is popular among Tory grassroots
Foreign Secretary Liz Truss is popular among Tory grassroots POOL via AFP / Ben STANSALL

However, such surveys can be highly volatile and relatively little is known of Mordaunt, despite her being the first female defence secretary and a current trade minister.

Following a succesful campaign launch Wednesday, she was brought down with a bump on Thursday when David Frost, the government's former Brexit pointman who remains influential among grassroots Tories, launched a scathing attack.

Mordaunt was a strong Brexit supporter and key figure in the 2016 "Leave" campaign, but Frost told TalkTV that "I would have grave reservations" about her becoming leader.

"I'm afraid she wasn't sort of fully accountable, she wasn't always visible. Sometimes I didn't even know where she was," he said of working with her on post-Brexit dealings with the EU last year.

Conservative MP Olukemi Badenoch has one of the lowest profiles of the current contenders
Conservative MP Olukemi Badenoch has one of the lowest profiles of the current contenders UK PARLIAMENT via AFP / Chris McAndrew

The former magician's assistant has promised a return to Conservative policies of "low tax, small state and personal responsibility" and a "relentless focus on cost-of-living issues".

Foreign Secretary Truss launched her campaign on Thursday, pointing to her credentials on Brexit and Ukraine while promising tax cuts.

She has also pointed to her competence on economic matters amid the current cost-of-living crisis after serving in the finance ministry.

The 46-year-old has attracted the support of Brexit-supporting Johnson loyalists in the cabinet and is popular among Conservative members for her outspokenness.

But that has also stoked questions about her judgement, for instance when in February she encouraged Britons to fight in Ukraine.

Despite the high-profile support, she has so far failed to coalesce Brexit-backing MPs around her.

Critics say her leadership posturing has been too overt and question her principles, after she campaigned against Brexit in 2016 only to later ally herself with the Tory right.

When she headed the Department for International Trade, some MPs dubbed it the "Department for Instagramming Truss" because of her prolific output on the social media site.

Former equalities minister Badenoch, who resigned last week, has been the surprise package of the campaign, rising from relative obscurity to see off high-profile candidates such as former foreign minister Jeremy Hunt and finance minister Nadhim Zahawi.

The 42-year-old, who spent much of her childhood in Nigeria, is a trenchant critic of "identity politics", a supporter of Brexit and a strong defender of conservatism.

Her campaign received a boost with the endorsement of Tory heavyweight Michael Gove.

The prominent backbencher who chairs parliament's influential foreign affairs committee was the first to launch his bid.

A former army officer who served in the Middle East, he is also a hawk on China and has been critical of the government's handling of the troop withdrawal from Afghanistan.

The 49-year-old committed to spending 3.0 percent of GDP on defence as he launched his campaign on Tuesday.