The Government has reportedly caved to backbench Tory rebels and agreed to amend its controversial Illegal Migration Bill, allowing ministers to ignore European judges in certain situations.

A group of Conservative MPs say they have reached a deal with Prime Minister Rishi Sunak to change new rules for removing people who arrive in the UK on small boats after threatening to revolt over the legislation, according to reports.

Danny Kruger, who is on the right of the party and among those leading the calls, said he was “grateful to the Prime Minister and the Home Secretary for their work”, the BBC said.

A source close to the MPs reportedly said ministers had agreed to give the Home Secretary powers to disregard injunctions from the European Court of Human Rights – so-called Rule 39 orders – in some instances.

The source indicated a second amendment will also be introduced requiring British judges to decide a deportation would cause “serious and irreversible harm” in order to block it.

The Government is expected to publish the amendments, which have been leaked to outlets including The Sun, The Times and the BBC, on Thursday ahead of debates and votes next week.

The Bill has been at the centre of controversy, with critics warning the proposed legislation leaves the UK foul of its international obligations and opposition parties dismissing it as unworkable.

But right-wing Tory MPs have signalled it does not go far enough, with some calling for ministers to take the UK out of the European Convention on Human Rights (ECHR) to drive through tighter border controls.

Others on the liberal wing want to see the Prime Minister commit to establishing safe routes via which asylum seekers can come to Britain.

The apparent compromise comes after Mr Sunak failed to guarantee he could achieve his plan to “stop the boats” by the next election and said it “won’t happen overnight”.

He had pledged to “stop the boats” as one of the five main priorities of his leadership.

But asked in an interview with Conservative Home whether he was confident he could do that by the next election, the Prime Minister said: “I’ve always said this is not something that is easy; it is a complicated problem where there’s no single, simple solution that will fix it.”

The Government’s Illegal Migration Bill is aimed at changing the law to make it clear people arriving in the UK illegally will not be able to remain in the country.

They will either be sent back to their home country or to a nation like Rwanda with which the UK has a deal, although legal challenges mean no flights carrying migrants have taken off for Kigali.

More than 5,000 migrants have arrived in the UK after crossing the Channel this year.

Home Office divs published on Tuesday confirmed the provisional number of people making the journey to date in 2023 stands at 5,049.

A Government spokesperson said: “The Prime Minister and Home Secretary are focused on delivering the five priorities for 2023 – halving inflation, growing the economy, reducing debt, cutting waiting lists and stopping the boats.

“While we have been clear there is no silver bullet, our Stop the Boats Bill will ensure anyone arriving illegally will be detained and swiftly removed, ending the unfair practice of people skipping the queue.”