British Prime Minister Rishi Sunak’s leadership of the governing Conservative Party is facing turmoil on Thursday after a bruising Cabinet resignation and open attacks by backbenchers over his government’s controversial policy to deport illegal migrants to Rwanda.

The 43-year-old British Indian prime minister is caught in the middle of two strands within his party, one on the extreme right voiced by sacked home secretary Suella Braverman calling for an extreme agenda to override legal challenges and the other more centrist view of the UK not being seen to breach its human rights obligations.

The clash came to a head on Wednesday night when Robert Jenrick, someone seen as a Sunak ally, resigned as his Immigration Minister, declaring that his boss’ new Safety of Rwanda Bill designed to override a Supreme Court block “does not go far enough”.

"I cannot continue in my position when I have such strong disagreements with the direction of the government's policy on immigration," wrote Jenrick in his resignation letter to Sunak.

Describing the small boat crossings across the English Channel by illegal migrants as doing "untold damage" to the country, Jenrick insisted that the government needed to get much tougher against “highly contested interpretations of international law".

"I have therefore consistently advocated for a clear piece of legislation that severely limits the opportunities for domestic and foreign courts to block or undermine the effectiveness of the policy. A bill of the kind you are proposing is a triumph of hope over experience," he added.

In his reply letter, Sunak countered by saying that the new bill would be "the toughest piece of illegal migration legislation ever put forward by a UK government" and that his former Cabinet ally’s opposition to it was "based on a fundamental misunderstanding of the situation".

"If we were to oust the courts entirely, we would collapse the entire scheme. The Rwandan government has been clear that they would not accept the UK basing this scheme on legislation that could be considered in breach of our international law obligations. There would be no point in passing a law that would leave us with nowhere to send people to," he claimed.

The resignation came soon after a blistering speech by Jenrick’s former boss in the Home Office, Braverman, who made a statement in the House of Commons to warn that the Tories under Sunak’s leadership faced “electoral oblivion in a matter of months” unless he sped up a crackdown on illegal immigration.

On Thursday morning, she followed this up by calling on the prime minister to “change course” before it is too late.

"I urge the prime minister to change course and change policy… (because) ultimately this bill will fail," she told the BBC.

"He said he would do whatever it takes. I'm telling him there is a way to succeed in stopping the boats and fulfilling that promise. If we do it, if he does it as prime minister, he will be able to lead us into the next election telling the people we have succeeded on this very important pledge," said the Goan-origin minister, who was sacked by Sunak last month as home secretary amid growing policy differences.

The new Rwanda draft bill, to be tabled in Parliament on Thursday for debate, compels UK judges to treat the African nation as a safe country and gives ministers powers to disregard sections of the Human Rights Act.

It follows the visit of Secretary of State for the Home Department James Cleverly to Kigali earlier this week to sign a new treaty with Rwandan Minister for Foreign Affairs Dr Vincent Biruta.

Under the plan, the UK plans to deport illegal migrants to Rwanda while their asylum claims are processed and hopes it will act as a deterrent for people smugglers bringing migrants illegally to UK shores.

Although the bill allows ministers to dis-apply sections of the Human Rights Act, it does not disregard the entire legislation, as some had demanded, and it does not include powers to dismiss the whole of the European Convention on Human Rights (ECHR).

"You can't tweak this problem. We can't do half-measures. We have to exclude international law – the Refugee Convention, other broader avenues of legal challenge," claims Braverman, a former barrister.

The latest row comes as Sunak continues to try and finetune his pitch for a general election expected in the next 12 months, amid a deeply divided Conservative Party which has seen prime ministers come and go in recent years due to infighting.

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