Rishi Sunak hopes an economic recovery can help chase down Labour in opinion polls. UK PARLIAMENT via AFP/Jessica TAYLOR

Tory MPs have criticised Prime Minister Rishi Sunak's leadership, telling reporters that they hope he will step down from his post to avoid damaging the reputation of the Conservative Party.

According to an anonymous former minister, several Conservative MPs have said that they were looking towards the local elections, set to be held in May this year, as a potential end to Sunak's time in office.

"This will be the crunch moment for a lot of those groups. That's stick or twist time," the former minister told reporters, noting that Sunak has "had a go for 18 months and the plan isn't working".

"If the locals go badly, I would very much expect someone to launch a serious attempt to remove the PM. If Rishi is still PM on 31 May, he will be PM at the election," they added.

According to the source, the rebel MPs had contacted Graham Brady, the Head of the 1922 Committee of backbench Tories, calling for the prime minister's resignation. However, the former minister also said that the group of Conservative MPs had not sent in their letters of no confidence yet.

The source went on to clarify: "Quite a lot of moderate MPs now agree with the traditional anti-Rishi types to say that the best course of action is not for us to remove him, but for him to stand down voluntarily, and they're speaking to Graham Brady about it. That's why you're not hearing much noise about it."

This news comes after Sunak's Downing Street showed no urgent calls for change after the Tories faced two heavy byelection defeats last week.

Since the Labour Party, spearheaded by Sir Keir Starmer, overturned the Conservative majorities by winning seats in Kingswood and Wellingborough, right-wing MPs have urged Sunak to knuckle down on immigration and tax cuts.

After Reform UK, formed by Nigel Farage, won more than 10 per cent of votes in both constituencies, Sunak was again, called upon to step up his controversial 'stop the boats' campaign and emergency Rwanda Policy.

Despite Sunak saying that the results showed that his party has "work to do", the former minister said: "No 10 think they're not in much trouble at all over a [leadership] challenge, which feels a bit arrogant."

With reference to the anonymous group of rebel MPs, one Tory backbencher also told reporters: "I haven't detected any signs from colleagues that we need to change the leader. Yes, some disagree on policy, but most people recognise that changing leaders literally months from an election is not a particularly good strategy."

"I would quietly say to anyone unhappy with Rishi: he's going to be going sooner or later anyway, most likely to the board of an investment bank, so you might as well wait for an election defeat," the long-serving MP said.

In a bid to win votes at the next general election, expected to take place before January next year, another former cabinet minister for the Conservative Party recognised that voters "don't like divided parties".

"If anyone thinks the byelections mean we need to change leader, they're taking the completely wrong lesson from them," they added.

Arguing that moving to the right on immigration legislation will not help win leadership votes, the former minister recalled: "When we have won elections, we have done so from the centre-right. So arguing that the answer is a leader who moves further to the right is also missing the point."

While Starmer said that he was "proud" of overturning the majorities of 11,220 in Kingswood and 18,540 in Wellingborough, the left-wing leader said that he did not "want to get into the warm bath of saying: 'Job done'".

However, it is clear that the country is "crying out for change", the Labour Leader added.