Rishi Sunak needs to win back Tory voters who have gone “on strike” because of the failure to curb immigration and tackle extremism, former minister Robert Jenrick said.

The Prime Minister needs to ensure Conservatives who stayed at home rather than vote in the local elections came back to the ballot box at the national contest later this year.

He also needs to win back Tories who have drifted to Reform UK because of concerns over immigration, Mr Jenrick said.

The Conservatives suffered a mauling from the electorate in last week’s contests, losing nearly 500 council seats, the West Midlands mayoral race and the Blackpool South by-election.

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Mr Jenrick, who quit as immigration minister in protest at Mr Sunak’s leadership on the issue, said there needed to be “some introspection” following the “very bad results” in the local elections.

The Newark MP, who has produced a paper on measures to curb net migration, said: “What I’ve tried to set out are a series of policies that could be implemented before the general election, such as what I’m saying today on legal migration, which would convince some of those Conservative voters – who are essentially on strike – to come back and support the party at the general election.

“And also to persuade some of those voters who are considering voting Reform that we do care about the issues that they do, which are principally immigration, but also on crime, on extremism and on lower taxes.

“And if we can do that, I think we can persuade more of those former Conservative voters to come back and to support us.

“But that will require honesty, it requires levelling with the public about the mistakes of the past and using every last minute we have in office before the general election to actually deliver positive change for the public.”

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At Tuesday’s Cabinet meeting, Michael Gove warned right-wing Tories against “comfort eating” by pursuing hardline policies that “make us feel good about ourselves”.

The Times reported that he told ministers: “As Kate Moss once said ‘nothing tastes as good as skinny feels’.”

Asked about his comments, Cabinet minister Claire Coutinho insisted the Tories were aligned with the priorities of the British public despite the drubbing they received in the local contests.

She acknowledged the local election results were “disappointing” but said “I do think we have a positive message that we need to communicate to people”.

Asked if the party should shift to the right, the Energy Secretary told Times Radio: “I think what we need to do is to go where the country is.”

She added: “They want us to be tough on immigration. They want us to be cognisant of the fact that they’ve had a difficult time when it comes to public finances, which is why we’re putting forward £900 of tax cuts.

“They want us to make sure that we’re protecting their security, which we are when it comes to defence, when it comes to energy as well.

“I would just have contrast with some of Labour’s positions, when it comes to their mad energy plans which will hike up people’s bills and heap costs on people, with the 75 new business regulations which will deter investment at a time when we need investment coming into this country and on things like immigration where they don’t have a plan at all.”