Rapidly rising prices and tax increases in the spring, followed by a drubbing for the Tories in May’s local elections, will mark the beginning of the end of Boris Johnson’s premiership, senior Conservative MPs now believe.

After Johnson suffered a massive rebellion by his backbenchers over Covid rules in the Commons on Tuesday and a humiliating byelection loss to the Liberal Democrats in the previously safe Conservative seat of North Shropshire two days later, the prime minister is being told he has only three to four months to turn things around or risk being ousted.

The news of Brexit minister Lord Frost’s shock resignation from the cabinet, which broke late on Saturday night, has not helped matters.

While MPs from all wings of the party agree that with the Omicron variant spreading like wildfire, now is not the time to strike, many are beginning to fear for their own seats at the next general election, and say May will be the decisive moment. Frustration is deep and anger is running high, but MPs say they must hold off for the time being.

One former minister said: “If there was not a pandemic I would be writing and signing my letter now and sending it off to Graham Brady [chair of the 1922 Committee of Conservative backbenchers] to trigger a leadership contest. And I think most of us would do the same.”

Another former minister said that while MPs were agreed that Johnson should be given time to recover ground in the new year, after a disastrous period in which sleaze and scandals of rule-busting No 10 parties have dominated headlines – few had any confidence that he would change.

The former minister said: “Boris isn’t willing to bring in new people, he isn’t willing to re-engage with the parliamentary party, he isn’t willing to do the hard graft, he isn’t willing to do the detail.

“Everybody is saying: ‘Let’s go through the process of giving him the opportunity to change’, but we all know where this is going and it is not pleasant. We are heading towards a leadership challenge. The next yardstick is the local elections.”

Martin Vickers, a Johnson loyalist and member of the 1922 Committee executive, said he was “confident” that the PM could reassert the strong leadership he showed before the 2016 Brexit referendum and 2019 election, but added: “He has got to do that straight away and avoid the drift of the last few weeks.”

Charles Walker, a former vice-chair of the 1922 committee executive, said it would be “unconscionable” to try to get rid of Johnson in the next few weeks, but warned of tough times ahead as the cost of living increases.

“The next six months are going to be extremely challenging for a variety of reasons, but mainly Omicron and the impact that yet another iteration of this virus will have on already fractured supply chains and the cost of living,” he said.

“The Conservative party is not in a position to have a leadership contest in these circumstances. It is just not conscionable. Having said that it is clear that over the next three months we cannot have a rerun of the past three months.”

Tory grandee Sir Roger Gale last week became the first Conservative to say he had sent his letter to Brady. Under party rules, if the committee chairman receives 54 letters in favour of a vote of no confidence in Johnson, he will be required to stage one.

If UK voters now begin to blame the government for rising prices, Tories fear a change at the top could be their only hope.

Next spring the government will come under pressure from a combination of tax increases and rising prices that will eat further into living standards.

In April, the energy regulator Ofgem is expected to allow a significant rise in the gas price cap that protects millions of households from volatile wholesale prices. Several high-profile gas suppliers have gone bust in recent months after they were unable to stem losses from supplying households with energy at below market prices.

In the last year gas prices on international markets have risen threefold. While the cap will continue to operate, the regulator is expected to judge that suppliers should be allowed to increase prices significantly.

Ministers agreed last week that rail fares would rise by 3.8% in March, despite warnings from several backbench Tory MPs that only a freeze on fares would encourage passengers to return to rail travel following an exodus triggered by Covid-19.

At the budget in October the chancellor, Rishi Sunak, said a 1.5 percentage point increase in national insurance contributions would take effect in April 2022, costing someone earning £20,000 an extra £120 a year.

The rise in national insurance will go to fund the health service and social care, but councils must wait until 2023 before any of the extra income is diverted from health budgets to social care funding.

Meanwhile Angela Rayner, Labour’s deputy leader and shadow chancellor of the Duchy of Lancaster, called on the prime minister to publish the terms of reference that have been given to the senior civil servant Sue Gray, following her appointment to oversee inquiries into social gatherings in Downing Street and other government properties over Christmas last year.

Gray was appointed after cabinet secretary Simon Case stepped aside, after it was revealed a party was held in his own offices in Downing Street last December.

Rayner said: “The public must be assured this is a genuine, new and empowered investigation that will get to the bottom of any misconduct by ministers and their advisers, publish its findings in full and hand evidence to the police.

“There are still too many questions unanswered about this murky affair and the prime minister should come clean right now.”