Rishi Sunak faces the most perilous week of his leadership as the fate of his flagship Rwanda Bill lies in the hands of two warring Tory factions.

The Prime Minister’s authority is under threat as tribes from the left and right of the Tories hold separate meetings to consider if they will back the beleaguered legislation in a crunch vote on Tuesday.

Hardline Brexiteers from the European Research Group and other camps on the Conservative right will first hold a summit on the legislation aimed at reviving his asylum policy.

Veteran MP Sir Bill Cash will present the findings of his so-called “star chamber” of lawyers, but he has already signalled they do not believe the proposed law is fit to get the grounded £290 million scheme up and running.

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

The Prime Minister 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.

Read more: Rishi Sunak's Rwanda plans risks angering Tory right over ECHR powers

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 that the UK 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.

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

Read more: Rishi Sunak told Rwanda plan that could seal his fate 'will not work'

The UK 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 for people seeking to cross the English 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.

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, that 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 UK Government to counter claims by right-wing critics.

The Prime Minister 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.

The proposed legislation seeks to allow 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”.

Read more: Immigration minister Robert Jenrick quits over Sunak's Rwanda plan

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.

However, Mr Sunak only needs a rebellion of 28 Conservatives to see his majority destroyed as Labour will vote against it.

A defeat would shred the Prime Minister’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.

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 would pass through the Commons “for sure” but that “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.