Boris Johnson has announced plans to end the legal requirement to self-isolate after a positive Covid-19 test as he moves to scrap the last remaining virus restrictions in England.

The UK prime minister, who is attempting to raise Conservative morale after being battered by weeks of Tory divisions, won cheers from his MPs as he suggested the worst of the Covid crisis was coming to an end.

“It is my expectation that we’ll be able to end the last domestic restrictions, including the legal requirement to self-isolate if you test positive, a full month early,” Johnson said at Prime Minister’s Questions in the House of Commons.

The prime minister, who was hit on Wednesday by criticism from a leading party donor, said he expected to set out a “living with Covid” plan when MPs returned from a break on February 21. The remaining legal restrictions were not due to expire until March 24.

Johnson set out his thinking last month when he said: “There will soon come a time when we can remove the legal requirement to self-isolate altogether — just as we don’t place legal obligations on people to isolate if they have flu.”

“As Covid becomes endemic we will need to replace legal requirements with advice and guidance urging people with the virus to be careful and considerate of others.”

Johnson’s comments helped to raise Conservative spirits. The prime minister’s support for lockdowns and other restrictions over the past two years inflamed tensions on the libertarian wing of his party.

The prime minister hoped a “reset” of his government — including a ministerial reshuffle — would reassure his party.

Earlier a leading Tory donor agreed with the suggestion that Johnson was “past the point of no return”. John Armitage, co-founder of the hedge fund firm Egerton Capital, told the BBC he found the current situation “tremendously upsetting”.

Armitage had given the Conservatives more than £500,000 since Johnson became prime minister, but also donated £12,500 last year to the Labour party. He said leaders should quit if they lost their moral authority.

Johnson was heavily criticised this week for his false claim that Sir Keir Starmer, Labour leader, “spent all his time” as director of public prosecutions failing to prosecute the late paedophile Jimmy Savile.

Johnson again rejected Labour calls to apologise, claiming that it would be wrong to “let the thugs and yobs who bullied and harassed” Starmer outside Westminster this week “off the hook” for their behaviour.

The prime minister was also challenged by former Tory chief whip Mark Harper to promise at the despatch box that the full report by civil servant Sue Gray into Whitehall lockdown parties would be published “immediately and in full” as soon as a police investigation concluded.

Johnson said he would publish “in full” whatever report Gray gives him. The police investigation into parties — including Johnson’s involvement in them — and the Gray report still hangs over the prime minister.

During the end-of-term exchanges, Starmer repeated his demand that Johnson levy a windfall tax on oil and gas companies to help cut rising domestic fuel bills.

Johnson said the companies needed to make profits to pay for a “transition” to low carbon energy, including more investment in gasfields in the North Sea while the shift to greener energy took place.