Boris Johnson on Monday refused to give his backing to any candidate vying to replace him as British prime minister, in his first public appearance since being forced to quit.

The 58-year-old leader dramatically announced his departure as Conservative party leader last Thursday, but is staying on in Downing Street until a replacement is found.

So far, 11 hopefuls have declared their intention to stand in the internal leadership contest, with the party expected to outline a timetable later on Monday.

On a visit to a science research institute in London, Johnson was asked directly if he would endorse a successor.

"The job of the prime minister at this stage is to let the party decide, let them get on with it, and to continue delivering on the projects that we were elected to deliver."

Johnson's fall from grace has been spectacular. In December 2019 he won a landslide 80-seat victory on a promise to take Britain out of the European Union.

His parliamentary majority allowed him to do just that but his premiership was hit by waves of scandal, not least about lockdown-breaking parties in Downing Street that saw him fined by police.

Another row blew up last week about his appointment of a senior colleague despite knowing of sexual assault allegations against him, sparking a frenzy of resignations and forcing Johnson to quit.

In his resignation speech, he blamed the "herd" for moving against him, and his allies have been briefing angrily against former chancellor of the exchequer Rishi Sunak.

But Johnson refused to say Monday whether he felt betrayed.

"I don't want to say any more about all that," he said. 

"There's a contest under way and that has happened and you know, I wouldn't want to damage any chances by offering my support. 

"I just have to get on and in the last few days or weeks... the constitutional function of the prime minister in this situation is to continue to discharge the mandate. And that's what I'm doing," he added. 

"The more we focus on the people who elect us... (and) the less we talk about politics at Westminster, the generally happier we will all be."

Among the frontrunners in the leadership race are Sunak and Sajid Javid, whose departures as finance minister and health minister sparked the flurry of more than 60 government resignations.

Foreign Secretary Liz Truss and Sunak's successor Nadhim Zahawi are also running. Home Secretary Priti Patel is reportedly mulling a bid too.