Rishi Sunak is calling for changes to the international law which experts think his Illegal Migration Bill will break.

The prime minister is in Iceland for a Council of Europe summit on Tuesday, where he will meet with heads of European Union countries and the European Court of Human Rights (ECtHR).

Mr Sunak said the “current international [migration] system is not working”, and that “our communities and the world’s most vulnerable people are paying the price”.

Downing Street is taking aim at rule 39 of the ECtHR in particular.

This is the procedure that allows the court to stop the “expulsion or extradition of people” – and was the power used to prevent the government from deporting people to Rwanda last year at the eleventh hour.

The ability of an institution based in Europe to make such directions has long drawn the ire of certain factions of the Conservative Party, although the court itself is not part of the EU.

Mr Sunak’s Illegal Migration Bill – currently making its way through the House of Lords – is set to allow the home secretary to ignore orders made under rule 39.

While this has been welcomed by Eurosceptic and anti-migration Tories, bodies like the Bar Council and the Law Society said taking such action would be a breach of international law and damage the UK’s international reputation.

Richard Atkinson, the deputy vice president of the Law Society, said: “If the UK were to refuse to comply with a European Court of Human Rights ruling this would entail a clear and serious breach of international law.

“The rule of law means governments respect and follow domestic and international law and disputes are ruled on by independent courts.”

The government has insisted that the bill complies with international law.

A source told Sky News that “rule 39 is the interim order used by Strasbourg judges to block the Rwanda flight last year,” adding that “it’s a novel legal mechanism”.

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It is with that background that Mr Sunak will make that case for “reform to the ECtHR’s rule 39 process to ensure proper transparency, greater accountability and ensuring decisions can be reconsidered”.

Downing Street say for the Illegal Migration Bill to function properly, it “must go hand in hand with international cooperation to establish a global asylum framework fit for purpose”.

Mr Sunak will discuss the reform of the ECtHR – including rule 39 – with the court’s president, Siofra O’Leary, during his time in Iceland.

The prime minister said: “It is very clear that our current international system is not working, and our communities and the world’s most vulnerable people are paying the price.

“We need to do more to cooperate across borders and across jurisdictions to end illegal migration and stop the boats.

“I am clear that as an active European nation with a proud history helping those in need, the UK will be at the heart of this.”

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According to immigration minister Robert Jenrick, the court is already carrying out a review of rule 39 “at the encouragement of a number of member states, including [the UK]”.