Boris Johnson and Priti Patel are among the senior Tory MPs backing a bid to ignore the European Court of Human Rights and start deportation flights to Rwanda immediately.
Conservative MP Jonathan Gullis will present a bill to parliament on Wednesday aimed at circumventing the Strasbourg court, which has blocked the controversial scheme from taking off.
It is likely to pile pressure on Rishi Sunak as it has the backing of high-profile Tories including Mr Johnson, the former prime minister, and Ms Patel, the former home secretary.
Ms Patel announced plans to deport asylum seekers to the east African country in April to crack down on Channel crossings, but although the government has paid Rwanda £140m, no flights have taken off yet due to a series of legal challenges over the summer.
Many Tory MPs expressed anger after an eleventh-hour intervention by the ECHR in June blocked the first scheduled deportation.
Mr Gullis told The Telegraph that his Asylum Seekers (Removal to Safe Countries) Bill will make sure “the final say on legislative matters lies in Parliament, not judges in a quasi-legislative supranational court in Strasbourg”.
The MP for Stoke-on-Trent North will present his plans through a Ten Minute Rule Bill, which allows a backbench MP to make their case for a new bill in a speech lasting up to ten minutes.
Former cabinet ministers Nadine Dorries and Jacob Rees-Mogg also support the legislation.
Mr Sunak has vowed to crackdown on immigration, and on Tuesday unveiled a raft of laws aimed at stopping people crossing the Channel.
He said this would include restarting the Rwanda plan, which has been widely criticised by opposition parties, refugee charities and the Archbishop of Canterbury.
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Nasar Abdollahi, an Iranian asylum seeker, has told Sky News how he “wanted to die” when he was put on the grounded flight to the country after arriving in the UK by small boat – and is still living in fear he could be sent there.
“If they’re going to send me to Rwanda I wish I’d stayed in Iran and they’d just killed me there,” he said.
A decision is due imminently on whether the government’s plan to send migrants to Rwanda is lawful.
The Home Office argues that the Rwanda scheme will help break the business model of people smugglers facilitating illegal immigration, but critics have raised concerns about human rights abuses in Rwanda and say there is no evidence it will deter the influx of Channel crossings.
More than 40,000 migrants have crossed the Channel this year – a huge increase on 2021, when it was fewer than 29,000.