Former UK finance minister Rishi Sunak says he is running to replace Boris Johnson, three days after helping to launch the cascade of resignations that brought the prime minister down.

Johnson announced on Thursday that he would stand down as prime minister after a mass rebellion in his Conservative Party, triggered by the latest in a series of scandals that had fatally undermined public trust.

Johnson’s imminent departure has added political uncertainty to an already difficult mix of soaring inflation, slowing growth and industrial unrest, set against a backdrop of war in Ukraine and the UK’s ongoing struggle to adapt to life after Brexit.

“Someone has to grip this moment and make the right decisions. That’s why I’m standing to be the next leader of the Conservative Party and your prime minister,” Sunak said in a campaign video released on Twitter.

Sunak and Health Secretary Sajid Javid quit the cabinet on Tuesday within minutes of each other, setting in motion a chain of events that led to Johnson’s decision to step down.

An opinion poll of Conservative Party members – who normally get to choose between the final two candidates – put Sunak in front on 25 per cent ahead of foreign secretary Liz Truss on 21 per cent.

The Opinium poll for Channel 4 News consulted 493 party members.

The rules and timetable for the contest to replace Johnson are due to be set out next week by a party committee.

Sunak’s budget last year put the United Kingdom on course for its biggest tax burden since the 1950s, which critics said undermined his claim to favour lower taxes.

During the COVID-19 pandemic Sunak oversaw about 400 billion pounds ($A701 billion) of economic support, avoiding a big jump in unemployment but letting public borrowing rise to a peacetime record high in the face of a historic slump in GDP.

Sunak’s popularity with Conservative MPs was later dented after he raised payroll taxes in April to fund higher health and social care spending, and announced plans to raise corporation tax sharply in 2023.

Sunak said in his resignation letter it had become clear that his approach to the economy had been too different to Johnson’s as the two had tried to agree on the next steps for the country.

He continued on that theme in his candidacy announcement video.

“The decisions we make today will decide whether the next generation of British people will also have the chance of a better future,” he said.

“Do we confront this moment with honesty, seriousness and determination? Or do we tell ourselves comforting fairy tales that might make us feel better in the moment, but will leave our children worse off tomorrow?”

The number of endorsements needed to enter the race has not yet been announced but one senior MP, Mark Spencer, who has a ministerial role in charge of parliamentary business, immediately announced his backing.

“In serious times we need a person with a proven track record. Rishi gets my full support,” he said on Twitter.

Sunak voted to leave the European Union in 2016.