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Rishi Sunak will face one of the greatest challenges of any new leader when he becomes British prime minister, needing to tackle a mounting economic crisis, a warring political party and a deeply divided country.

The 42-year-old former finance minister becomes Britain's third prime minister in less than two months, after infighting and feuding at Westminster that has horrified investors and alarmed international allies.

The former hedge fund boss - and one of the richest politicians in parliament - will now need to find deep spending cuts to plug a STG40 billion ($A72 billion) hole in the public finances at a time when his party's standing in the country has plummeted.

He warned his Conservative colleagues on Monday that the party faced an "existential crisis" if it did not help to steer the country through what he described as a "profound economic challenge.

"We now need stability and unity, and I will make it my utmost priority to bring our party and our country together," he said.

Sunak, Britain's youngest prime minister for more than 200 years and its first leader of colour, will replace Liz Truss who resigned after 44 days following a "mini budget" that sparked turmoil in financial markets.

With debt interest costs rising and the outlook for the economy deteriorating, he will need to review all spending, including on politically sensitive areas such as health, education, defence, welfare and pensions.

His first task, after being appointed by King Charles at Buckingham Palace on Tuesday, will be to select a cabinet of senior ministers that some Conservative lawmakers hope will include politicians from all wings of the party.

He is expected to retain Jeremy Hunt as finance minister after the former foreign and health secretary helped to calm volatile bond markets by ripping up most of Truss's economic program.

Investors will also want to know if Sunak will stick to a plan to publish a new budget alongside borrowing and growth forecasts on October 31, which would help inform the Bank of England's next move on interest rates on November 3.

Sunak, a Goldman Sachs analyst who only entered parliament in 2015, will also need to unite his party, aware that voters are increasingly angry over the antics of politicians at Westminster as the economy heads for recession, spurred by rising energy and food costs.

Sunak was blamed by many in the party when he quit as finance minister in the summer, triggering a wider rebellion that brought down the-then leader Boris Johnson.

While many expressed relief on Monday that the party had settled on a new leader quickly, a sense of distrust remained among some while others questioned whether struggling families would relate, or ever vote, for a multimillionaire.

"I think this decision sinks us as a party for the next election," one Conservative lawmaker told Reuters on condition of anonymity.

Historian and political biographer Anthony Seldon told Reuters that Sunak had the most difficult economic and political inheritance of any British leader since World War II, and would be constrained by the mistakes of his predecessor.

"There is no leeway on him being anything other than extraordinarily conservative and cautious," he said.

After politicians and officials in foreign capitals looked on in horror as a country once seen as a pillar of economic and political stability embarked on a bout of brutal infighting, many welcomed Sunak's appointment as a fresh start.

His appointment also marks a first in Britain as Sunak, a Hindu, becomes its first prime minister of Indian origin.

© RAW 2022

King Charles III has appointed Rishi Sunak prime minister of Britain after the monarch accepted the resignation of Liz Truss who served just 49 days in office.

The new Conservative leader was invited to form a government by Charles when they met at Buckingham Palace on Tuesday after Truss departed as the shortest-serving prime minister in British history.

Sunak, 42, is the UK's first Hindu PM, the first of Asian heritage and the youngest for more than 200 years.

The former chancellor was expected to address the nation from Downing Street shortly after leaving the palace.

© RAW 2022

Brisbane have approved Chris Fagan's immediate return to AFL coaching ahead of the investigation into historic racism claims at Hawthorn.

New North Melbourne coach Alastair Clarkson also has returned from overseas and is looking forward to telling his side of the story in the saga.

But the four-time Hawks premiership coach remains unclear when he will officially start at the Kangaroos.

The Lions announced on Tuesday night their board had cleared Fagan to return to coaching on Wednesday.

It follows the AFL's release last Thursday of the terms of reference for the independent investigation of racism allegations at Hawthorn.

Senior lawyer Bernard Quinn KC was appointed on October 4 to lead the four-person panel.

Initial statements are due on November 4.

The investigation will include mediation if needed and the league is projecting it will end in December, with the resulting report to be made public.

Clarkson and Fagan stood aside from their coaching duties last month when the allegations were made public.

Clarkson has just returned from Scotland, where he spent time with Celtic soccer boss Ange Postecoglou, and welcomed receiving more details on the investigation.

"Yeah, it's taken a bit of time to get through that (finalising the terms of reference)," Clarkson told the Nine Network.

"At least we've got a platform now from which we can get a chance to tell our side of the story."

The claims centre on Clarkson's time at Hawthorn with his then-football manager Fagan and former welfare manager Jason Burt also named in an ABC report alleging racist behaviour at the Hawks.

Clarkson, Burt and Fagan, who has taken leave from his role as the Brisbane Lions coach, deny any wrongdoing.

"Fages (Chris Fagan), myself and Jason (Burt) have been through a tough time over the last four weeks," Clarkson said.

"I'm just pleased that they've been able to identify a platform in which we can reveal some of the truth behind this and then we get onto it.

"The bottom line is our most significant commitment that we need to address in the next little while is obviously the investigation.

"Fages, Jase and myself always said right from the get-go that we'd co-operate fully with whatever the AFL put in place."

If the investigation finds anyone should be subject to a discipline process, that would be a separate process under AFL rules.

There is still doubt over whether the parties that contributed to Hawthorn's cultural safety review will take part in the AFL's investigation.

Clarkson's initial start date at North Melbourne was November 1, but that was due to be pushed back and he wouldn't be drawn on his next steps.

"I just need to speak with our lawyers and also the AFL and the club," he said.

"If somewhere along the line we get the opportunity to return to work, then that would be great as well but our priority is to make sure that we co-operate fully with the investigation."

© AAP 2022