Rishi Sunak’s new Safety of Rwanda Bill should stop 99.5% of legal claims made by migrants to block their deportation, a minister has said.

The prime minister is trying to convince his own backbenchers to support the legislation – with both the right of the Conservatives and separately the One Nation caucus set to announce whether they support it later today.

Only 29 Tory MPs need to vote against the government – or 57 need to abstain – for the government to be defeated.

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The bill seeks to declare Rwanda a safe country, and also empower ministers to ignore parts of the Human Rights Act from being used to stop people from being removed from the UK.

Speaking to Sky News this morning, Defence Secretary Grant Shapps said: “The modelling suggests that of the current cases which are challenged successfully, 99.5% of them would not be challenged once this is in place.”

The minister – who was home secretary for less than a week during the political chaos in government last year – admitted it is “doubtless” the Safety of Rwanda Bill would be challenged in the courts.

The details of the bill are being examined by legal experts across the political spectrum, with the Tory right set to discuss their verdict at lunchtime on Monday.

Members of the European Research Group will be discussing their next steps like they did during Brexit, and have invited the likes of the New Conservatives, the Common Sense Group, the Conservative Growth Group and the Northern Research Group.

The ERG’s Sir Bill Cash, who is leading the investigation for the right, has already said the bill does not deliver on what is needed.

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And some within the Conservative Party claim the figure used by Mr Shapps is from an “outdated and analytically flawed model”.

A senior Tory source said: “This is an outdated and analytically flawed model – from March – which came before defeats in the Court of Appeal and Supreme Court.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 two months. It would be laughable if it wasn’t so serious.”

Some within the party have already stuck their head above the parapet to say they will not support the bill.

Robert Jenrick, who resigned as immigration minister last week, said he would be abstaining on Tuesday’s vote on the bill, with the hope of amending it at a later stage.

Writing in The Daily Telegraph, he said the idea it would “guarantee all those arriving are detained and swiftly removed is for the birds”.

He added the ability for individual legal challenges needed to be removed.

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Others – like former minister Neil O’Brien – have indicated they plan to support the government at the bill’s second reading on Tuesday, but then hope to amend it later.

Some One Nation Conservative MPs told the Politics at Jack and Sam’s podcast that parts of their group will vote against the government, while some on the right do not see a way of toughening the bill in a way that it could become law.