Some Conservative lawmakers have urged the British Prime Minister Boris Johnson to be replaced immediately rather than be allowed to remain as a caretaker leader until his successor is found.

Johnson announced his resignation as prime minister on Thursday after he was ditched by cabinet ministers and many Conservative Party's lawmakers who said he was no longer fit to govern.

Speaking outside his Downing Street office, Johnson announced his "painful" resignation but defied pressure to step down now, insisting he planned to stay on as prime minister while his party picks his successor.

But seven Conservative members of parliament demanded Johnson leave office immediately because he has lost his authority and said an interim prime minister should take over during a leadership contest, a process that could take weeks.

Dominic Raab, the deputy prime minister, would be a suitable replacement, several Conservative lawmakers said.

Former British prime minister John Major agreed that Raab could take over until a new leader is found, or the party could change the selection rules to speed up the process.

"The proposal for the prime minister to remain in office – for up to three months – having lost the support of his cabinet, his government and his parliamentary party is unwise, and may be unsustainable," he said in a public letter.

Meanwhile, Conservative MP Tom Tugendhat said he was launching his bid to succeed Johnson, the first candidate to announce their campaign since the premier announced his resignation.

In an opinion piece in the Daily Telegraph, Tugendhat – known as a China hawk who heads parliament's foreign affairs committee – confirmed his intention to stand for the leadership of the Conservative Party, saying he wanted to bring together a "broad coalition" for a "clean start".

"I have served before – in the military, and now in Parliament. Now I hope to answer the call once again as prime minister," he wrote.

The prime minister's decision to quit marks the end of a rollercoaster political career in which he led Britain out of the European Union and took his Conservative Party to the largest election victory in three decades.

It follows three years of scandals, including anger over parties held at his Downing Street office during the coronavirus lockdowns, accusations of breaking international law over his threat to override parts of the treaty governing Britain's exit from the European Union and, most recently, his handling of sexual harassment allegations against a lawmaker. (Agencies)