MPs on the Tory right have gathered to consider Rishi Sunak’s beleaguered Rwanda Bill in the first of two meetings between warring Conservative factions which pose one of the biggest challenges of his premiership yet.

The Prime Minister’s authority is in the hands of tribes from the right and left as they hold separate meetings on Monday to consider backing the legislation in a crunch vote on Tuesday.

Veteran MP Sir Bill Cash is presenting the findings of his so-called “star chamber” of lawyers tasked with scrutinising the Bill to hardline Brexiteers from the European Research Group and other camps on the Conservative right.

The assessment is expected to deem the scope of the legislation too narrow to get the grounded £290-million scheme up and running as it stands.

Mr Sunak has tried to find a middle ground in response to the Supreme Court ruling that his plan to send asylum seekers who arrive in the UK on small boats is unlawful.

His Bill allows ministers to disapply the Human Rights Act but does not go as far as overriding the European Convention on Human Rights, with Sir Bill already signalling that stronger measures are deemed necessary to prevent further legal setbacks.

Former home secretary Suella Braverman, Mark Francois, Lord Frost, Richard Drax and Christopher Chope were among the Conservatives to turn up at the summit in Parliament’s Grimond Room.

Later, the more moderate wing of One Nation Conservatives will hold a separate evening meeting in Parliament before releasing a statement on their judgment.

Mr Sunak will be unable to focus fully on seeking to unite his fractured party as he spends Monday giving evidence to the UK Covid-19 Inquiry, where he will be questioned on his controversial Eat Out to Help Out scheme.

But top ministers, including Foreign Secretary Lord Cameron, have been engaging with MPs over the weekend in order to quell any rebellion over the Rwanda plan.

Defending the plan on the morning broadcast round, Defence Secretary Grant Shapps insisted it would prevent the vast majority of attempts to use the courts to avoid being sent to the African nation.

He said the Government’s current assessment is that only one in 200 cases will pass through once the Bill becomes law, following claims the analysis dated back to March.

Mr Shapps said: “My understanding is it’s current … I don’t have the precise details to hand.”

But critics of the plan dismissed the Home Office’s modelling of how effective it would be.

A senior Tory source said: “This is an outdated and analytically flawed model – from March – which came before defeats in the Court of Appeal and Supreme Court. Number 10 don’t realise the world has changed and that’s their fundamental problem.

“There was never any modelling done for the new Rwanda Bill because they failed to plan. Even this old, optimistic model says it could take more than two months to remove a migrant. It would be laughable if it wasn’t so serious.”

Mr Shapps rejected the suggestion Mr Sunak’s leadership is in chaos, telling BBC Breakfast: “A third down, in terms of crossings … the facts are we’re having success with it.”

The Government has insisted the Rwanda scheme, through which asylum seekers in the UK would be deported to Kigali, is a key part of Mr Sunak’s plan to “stop the boats” by acting as a deterrent to people seeking to cross the Channel.

But the Home Office has earmarked at least £700 million to manage the arrival of migrants on small boats until 2030, with the option of extending the contracts until 2034, according to commercial plans highlighted by the BBC.

The money will be spent running the Western Jet Foil facility in Dover and the reception centre at the former Manston airfield in Kent.

Home Office modelling, seen by The Times newspaper, which suggests 99.5% of individual legal challenges submitted by asylum seekers will fail to block their deportation under the Bill, will be used by the Government to counter claims by right-wing critics.

Mr Sunak’s Bill seeks to enable Parliament to deem Rwanda a “safe” country and block courts and tribunals from considering claims that the country will not act in accordance with the Refugee Convention or other international obligations.

Some on the right believe more radical measures are needed to cast aside international law, while moderates have concerns about its legal impact and about ordering courts to deem Rwanda a “safe” country.

Mr Sunak has told MPs the Conservatives must “unite or die” but it is unclear whether they will heed his warnings as some of his possible successors court the limelight.

Robert Jenrick, who resigned as immigration minister over the legislation, told the BBC on Sunday he will not support the “weak Bill that will not work”.

But he said “we can fix this”, raising the possibility he could abstain along with other opponents before trying to amend the legislation at a later stage.

Tuesday is the first opportunity for the Commons to vote on the legislation in what is called a second reading.

A Government Bill has not been defeated at this stage since 1986 but Tory MPs could abstain or seek to rewrite it at later stages.

A loss would shred Mr Sunak’s authority but One Nation chairman Damian Green said any Conservative who thinks they should change leader is “either mad or malicious or both”.

Conservative former solicitor general Lord Garnier, who has done the legal work for that group, has compared the Bill with ruling “all dogs are cats” by claiming Rwanda is safe.

This is the strongest possible piece of legislation to get Rwanda operational

He plans to oppose it in the Lords, where Mr Sunak’s battle is likely to be even greater, and has described it as making both political and legal “nonsense”.

Mr Shapps conceded on Monday that the Bill could face problems in the upper chamber but insisted it will pass through the Commons “for sure” but “sometimes you have to fight these things through”.

A legal assessment for the Government has given it only a “50% at best” chance of successfully getting flights to Kigali off next year as result of interim injunctions from Strasbourg.

A No 10 source echoed Mr Sunak by saying there is only an “inch” between the current policy and an overriding of elements of the European Convention on Human Rights, that he says would see the Rwandan government reject it.

“This is the strongest possible piece of legislation to get Rwanda operational,” they added.