The former home secretary warned the Tories they are in a “perilous situation” on tackling small boat crossings after the Prime Minister suffered the blow of the resignation of Robert Jenrick.
The immigration minister quit over Mr Sunak’s new emergency legislation to revive the policy by declaring Rwanda a safe country after it was deemed unlawful by the Supreme Court.
Mr Sunak carried out a mini-reshuffle on Thursday morning, splitting Mr Jenrick’s previous role into two by appointing Michael Tomlinson as illegal migration minister and Tom Pursglove as legal migration minister.
Mr Tomlinson, who was replaced as Solicitor General by Robert Courts, will attend Cabinet.
Mr Sunak’s decision not to go as far as overriding the European Convention on Human Rights has angered some hardliners, as the mood in the Conservative Party sours.
The Prime Minister will hold a Downing Street press conference at 11am on Thursday when he is expected to defend the legislation that give powers to disregard sections of the domestic Human Rights Act.
Mrs Braverman declared that “ultimately this Bill will fail” as she took to the airwaves to attack the plans of the Prime Minister who sacked her as home secretary last month.
She told BBC Radio 4’s Today programme that in the “very litigious field” of asylum law “the reality is and the sorry truth is that it won’t work and it will not stop the boats”.
Tweaks to the Rwanda plan will not be enough to get people on the plane to the East African nation, Mrs Braverman said, adding that the new legislation would still allow legal claims that could block flights and “clog up the system”, potentially for years.
“We can’t do half measures. We have to totally exclude international law – the Refugee Convention, other broader avenues of legal challenge,” she said.
Mrs Braverman, who said on Wednesday that the Conservatives faced “electoral oblivion in a matter of months” if they fail on the Rwanda policy, denied the Tories have a “death wish”.
But she said they are in a “very perilous situation”.
“The time for talk, the time for slogans and promises is over. We need to show delivery and that’s what this debate right now is all about,” she added.
She insisted she wants the Prime Minister to succeed, despite describing him as “weak” and “uncertain” in a scathing attack on his leadership after he sacked her.
But she said Mr Sunak would have to change course if he wants to lead the party into the next election.
Mr Braverman’s outspokenness on the issue and Mr Jenrick’s dramatic resignation signals a growing right-wing rebellion that could threaten Mr Sunak’s premiership.
The draft Bill unveiled on Wednesday compels judges to treat Rwanda as a safe country after the Supreme Court ruled the scheme was unlawful over risks to refugees.
The legislation, which must be voted on by Parliament, gives ministers the powers to disregard sections of the Human Rights Act.
But it does not go as far as allowing them to dismiss the European Convention on Human Rights, as hardliners including Mrs Braverman have demanded.
Mr Jenrick, an old ally of Mr Sunak, resigned just hours after the publication of the draft Bill, saying it “does not go far enough” and is a “triumph of hope over experience”.
Cabinet minister Chris Heaton-Harris attempted to play down Tory divisions over the Rwanda policy following Mr Jenrick’s departure.
Asked if the vote on the Safety of Rwanda Bill would be treated as a matter of confidence in the Prime Minister, the Northern Ireland Secretary told Sky News that was a decision for the whips but “I can’t see why it would need to be because I think all Conservatives will vote for it”.
Asked if the Prime Minister would face a confidence vote, Mr Heaton-Harris told LBC: “I think it’s highly unlikely, very unlikely. I’d say vanishingly small.”