Rishi Sunak will try to avert a mass rebellion by right-wing Tory MPs against his Rwanda plan, as he struggles to reconcile the competing demands of different Conservative factions.

Would-be rebels have warned the Prime Minister that “major surgery” is still required to fix the flagship asylum legislation, with as many as 40 MPs prepared to either abstain or vote against the proposed legislation in its first Commons vote on Tuesday.

Around 20 members of the New Conservatives will attend a breakfast with Mr Sunak in Number 10 later this morning, as ministers engage in a last-ditch attempt to win over party colleagues and avert a humiliating defeat at the second reading.

The grouping of mostly 2019 MPs warned on Monday, after a meeting at the office of backbencher Danny Kruger and attended by former ministers Robert Jenrick and Suella Braverman, that the Bill “needs major surgery or replacement”.

In a boost to the Prime Minister, One Nation moderates – numbering around 100 MPs – said that they would recommend backing the bill after attending a meeting addressed by Attorney General Victoria Prentis.

But the chairman Damian Green also warned that its MPs would oppose any amendments that would risk the UK breaching the rule of law and its international obligations.

He said: “We support the Bill unamended, but if anyone brings forward any amendments that breach our international obligations or breach the rule of law, we vote against those amendments at future stages.

“We will vote with the Government tomorrow, but we want the Government to stick to its guns and stick to the text of this Bill.”

Ministers are expected to continue to make overtures backbenchers over the course of Tuesday, with a vote in the Commons not expected until the evening.

No Government legislation since the Shops Bill in 1986 has fallen at second reading, but if all Labour and other opposition party MPs vote against it, a revolt by 29 Tories would be enough to defeat it.

Tories with concerns could instead choose to abstain or back the legislation at this stage but then seek to toughen it up – or water it down, depending on their views – as it progresses through the Commons.

A spokesman for the New Conservatives said: “More than 40 colleagues met tonight to discuss the Bill.

“Every member of that discussion said the Bill needs major surgery or replacement and they will be making that plain in the morning to the PM at breakfast and over the next 24 hours.”

Home Secretary James Cleverly used an article in the Telegraph to defend the plan overnight, writing: “After Brexit, the United Kingdom is a fully sovereign country once again – and of course we must control our borders. Anyone who agrees must support the Rwanda Bill.”

It came after he also addressed Tory MPs in an another briefing on Monday afternoon. Not long before, Conservative backbench European Research Group chairman Mark Francois had called on the Prime Minister to “pull” the legislation after lawyers convened by the caucus deemed it an “incomplete” solution to problems posed by small boat asylum claims.

The Bill allows ministers to disapply the Human Rights Act but does not go as far as overriding the European Convention on Human Rights.

The Government’s current assessment is that only one in 200 cases will successfully avoid being sent to Rwanda once the Bill becomes law.

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

Mr Jenrick, in a post on social media, doubled down on his rebuke of the plan: “If individual claims are permitted everyone will make one, the court backlog will balloon, our detention capacity will become overwhelmed within days, people will be bailed, and new arrivals will simply abscond.

“The proposed bill is both legally and operationally fundamentally flawed.”

Human rights group Amnesty International UK urged all MPs to vote against the legislation, calling it an “outrageous attack on the very concept of universal human rights”.

Chief executive Sacha Deshmukh said: “It should alarm politicians that the only way the Government thinks it can force through its doomed Rwanda policy is by removing basic protections and preventing the court from scrutinising its actions.

“This Bill is a threat to everyone’s human rights, because if the Government can recast the facts to serve its own purpose regardless of the reality, then there is no way for anyone to show their rights have been violated.

“We are urging all MPs in the strongest terms to take a stand against this outrageous attack on the very concept of universal human rights.”

Mr Sunak won support from former Cabinet colleague Ben Wallace, who used an article in the Telegraph to warn his party not to “wreck” the Government over the issue.

The former defence secretary said that the vote should not become an “exercise of making the perfect (but unrealistic) the enemy of the good”.