As British Prime Minister Boris Johnson faces the challenges of soaring virus deaths and looming Brexit talks, two of his closest aides have resigned amid reports of bitter infighting.

The British prime minister's top aide and the organiser of the "Vote Leave" campaign, Dominic Cummings, walked out of Downing Street on Friday holding a cardboard box.

This came a day after the resignation of Johnson's communications director Lee Cain, a close Cummings ally who also worked on the "Leave" side of the 2016 referendum.

Matters took another turn later Sunday when a Downing Street spokesman announced that Johnson had gone into self-isolation after someone he was in contact with tested positive for the Covid-19 virus.

"He will carry on working from Downing Street, including on leading the Government's response to the coronavirus pandemic," the Downing Street spokesman added.

Johnson, 56, was hospitalised in April after contracting coronavirus.

He spent three nights in intensive care, later crediting hospital staff with saving his life.

This time round "the PM is well and does not have any symptoms of COVID-19", the spokesman said.

While in isolation Johnson will no longer be able to turn to Cummings and Cain for advice.

While Cain was little-known to the British public, Cummings became massively unpopular in May when he failed to apologise for violating the government's strict coronavirus lockdown measures with lengthy road trips, while Johnson took his side.

Cummings had said he expected to stay until the end of the year and the final stage of Brexit.

After Johnson reshuffled his senior aides, some senior Tories said they hoped to see less "confrontational" relations between the prime minister and MPs.

But the Guardian called the sudden departures a "political pantomime," as the BBC reported the men would work out their notice at home.

Dominic Cummings (l) and Lee Cain have both resigned amid reports of bitter Downing Street infighting
Dominic Cummings (l) and Lee Cain have both resigned amid reports of bitter Downing Street infighting POOL / Adrian DENNIS

Former Brexit secretary David Davies in an interview with BBC television on Saturday alleged that Cummings' relationship with Johnson "fell off a cliff" after the prime minister's newly appointed spokeswoman, Allegra Stratton, and the prime minister's fiancee Carrie Symonds "turned against him."

Davies referred to Cummings' "very confrontational style."

The Daily Mail reported sources as saying that Johnson showed Cummings texts allegedly proving he had briefed against Symonds, formerly the head of communications for the Conservative Party.

The BBC reported that Cain resigned after opposition among MPs and ministers to his potential promotion to Johnson's chief of staff, while a source said Symonds had also spoken out against this.

Some MEPs suggested that the departure of hard-line Brexiteers might lead to Britain taking a softer stance in negotiations, especially after the US election defeat of Donald Trump, an ally of Johnson.

But those involved in crunch post-Brexit trade talks in the coming week insisted they would not be affected.

Irish Foreign Minister Simon Coveney told Sky News on Sunday that the drama had caused "huge distractions for Number 10 but they're not distractions for the EU."

"I don't think the departure of Dominic Cummings makes any particular impact on the negotiations," British Environment Secretary George Eustice told Sky News, stressing the talks had been led from the start by Britain's chief negotiator, David Frost.

"For those of us in the cabinet, we don't tend to immerse ourselves in the gossip of who said what to who," Eustice added.

Others in Britain criticised Johnson's team for their timing, however.

Liberal Democrat leader Ed Davey told the BBC it was "scandalous" that amid the pandemic, record redundancies and Brexit talks, "people in No 10 round the prime minister are arguing and jockeying for position."

Labour shadow health minister Jonathan Ashworth tweeted that as Britain's death toll from coronavirus reached 50,000, "the preoccupation of Boris Johnson is his squabbling spin doctors."

The Sun tabloid wrote in an editorial: "This is not the hour for national news to be dominated by office feuds."