Robert Jenrick said he was “not interested” in a bid for the Tory leadership amid speculation that discontent over the Government’s Rwanda plan could split the party.

The Conservative MP for Newark, who quit his role as immigration minister on Wednesday, defended his position on the need to reduce migration into the UK, warning a lack of integration means communities are “leading parallel lives”.

Mr Jenrick argued the Government’s proposed legislation on the plan to send asylum seekers to Rwanda does not go far enough, raising concerns over the likelihood of prolonged legal challenges.

In a sign of how seriously senior figures in the party are treating the threat of a challenge to Rishi Sunak’s leadership, Communities Secretary Michael Gove has sent a message to Tory MPs who are considering putting in letters of no confidence.

Mr Gove told the BBC’s Sunday with Laura Kuenssberg: “Let’s focus on the job.”

Amid speculation that Mr Jenrick is seen by some in the party as a potential replacement for Mr Sunak, the former immigration minister was asked on the BBC’s Sunday With Laura Kuenssberg if he would rule out running if there is a contest.

He said: “I’m not interested in that. I’m solely interested in this (migration) policy.

“I want the Conservative Party to win the next general election. I want it to make good on its manifesto commitments.

“I think there is a way to do that.”

But Mr Jenrick also said he would not support proposed legislation due to be considered by MPs in the Commons on Tuesday.

We've already done two Bills, this is the third Bill. It's three strikes or you're out

Asked if he would vote for the Rwanda Bill, he said: “No, I won’t be supporting this Bill, but I do think we can fix this, and that’s what I want to do now.

“I care about this policy because I care about border security and I’m determined that we can persuade the Government and colleagues in Parliament that there is a better way.”

He added: “We’ve already done two Bills, this is the third Bill. It’s three strikes or you’re out.

“I want this Bill to work and create that powerful deterrent and I’m afraid it’s very clear to all those people who really understand how this system operates that this Bill will not succeed.”

Mr Jenrick insisted the Prime Minister’s Bill will not work, adding: “We respectfully disagree on this one issue. I think that a political choice has been made to bring forward a Bill which doesn’t do the job.”

He said: “The test for this is not ‘can you get one or two symbolic flights off before the next election with a handful of illegal migrants on them?’, it’s ‘can you create a strong deterrent that is sustainable and stops the boats and protects the borders of this country for years to come?’

“That’s what I want to achieve and I’m afraid this Bill is not it.”

I am very worried that a million new people coming into our country every year is damaging our ability to integrate those people

He also said the electoral prospects of his party “hinge, in good measure” on addressing issues related to the levels of legal migration and asylum claims, warning a failure to do so will result in “the red-hot fury of the public”.

Senior Tory Damian Green attempted to dampen speculation over a leadership contest and hit out at the “very small number “of his colleagues who would support such a move.

He told the BBC: “It’s a vanishingly small number and anyone who thinks that what the Conservative Party or the country needs is a change in prime minister is either mad or malicious or both.

“And it’s a very, very small number doing that.”

Mr Jenrick also spoke about his concerns that the number of people coming to the UK is reducing the prospect for successful integration.

He told the BBC: “I am very worried that a million new people coming into our country every year is damaging our ability to integrate those people successfully and to be a united country.”

Asked for his evidence that integration is not working, he said: “I think there are communities in our country where people are leading parallel lives. And… it’s inevitable… it’s an obvious observation that a million people coming into our country every year is immensely challenging to successfully integrate.

“And I’m afraid you see that, I mean I’ve seen that recently, for example, with the marches through London where I saw some people who simply did not share British values.

“I thought that was wrong, it was deeply disturbing, and I think we’ve got to take action to address that.”

He added: “I think it’s connected to mass uncontrolled migration and I think we have to change that.”