Britain's former finance minister Rishi Sunak refused on Tuesday to criticise Prime Minister Boris Johnson, despite having helped trigger his dramatic downfall.

Sunak, 42, quit last week in protest at Johnson's scandal-hit administration along with another minister, setting off a wave of government resignations that forced Johnson to step down as leader of the Conservative Party.

Johnson is staying on in Downing Street as prime minister until an internal party contest finds his successor.

Officially launching his campaign, Sunak, who is seen as one of the frontrunners, called Johnson "one of the most remarkable people I've met".

"Whatever some commentators may say, he has a good heart," he told cheering supporters, after one Johnson ally accused Sunak of being a treacherous "snake".

"But did I disagree with him? Frequently.

"Is he flawed? Yes, and so are the rest of us.

"Was it no longer working? Yes, and that's why I resigned.

"But let me be clear, I will have no part in a rewriting of history that seeks to demonise Boris, exaggerate his faults or deny his efforts."

Johnson's departure was a spectacular fall from grace for a politician who secured a landslide general election win in December 2019 and took the country out of the European Union just a month later.

Sunak said he would not shy away from praising that or recognising Johnson's stewardship of the fightback against Covid or his hawkish support for Ukraine.

"Some people might advise that I should avoid saying all of this in case of alienating people but that wouldn't be honest," he added.

"If telling you what I think -- positive and negative -- costs me the leadership, so be it."

So far, 11 candidates, including Sunak, his replacement at the Treasury Nadhim Zahawi and Foreign Secretary Liz Truss are vying to replace Johnson.

A winner will be announced on September 5, after a series of votes by the parliamentary party and grassroots members.

In his pitch, Sunak, who if successful would become Britain's first Hindu prime minister, said he had a plan to steer the country through troubled economic times, not least the soaring cost of living.

But unlike several other candidates, he said it was "not credible to promise lots more spending and lower taxes".

And he rejected claims that as part of Johnson's tarnished administration, he was not the fresh start he was claiming.

He said he had responded to revelations about his wealthy wife, after it emerged she was not paying UK tax, and that he had a green card for US residency even while serving as chancellor of the exchequer.