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Rishi Sunak has warned migrants threaten to “overwhelm” countries including the UK unless radical action is taken – as he said he was prepared to push for reforms to global rules on refugees.

The prime minister also said that failing to tackle illegal migration would “destroy the public’s faith” in politicians and “our very systems of government” during a conference organised by the far-right Italian leader Georgia Meloni.

In his speech in Rome, he warned that “enemy” states were deliberately “driving people to our shores to try and destabilise our societies.”

And he invoked Margaret Thatcher’s “radicalism” as he tried to save his controversial plan to deport asylum seekers to Rwanda, which has come under fire from MPs on all sides of his party.

His comments appeared to echo the harder language on migration of his sacked former home secretary Suella Braverman. She was condemned last year for claiming the UK faced an “invasion” on its south coast.

It comes just a day after a death in the Channel caused opposition politicians to urge the government to do more to tackle illegal gangs.

While in Italy Mr Sunak will hold talks with Ms Meloni, and the leader of Albania, in which a crackdown on illegal migration is expected to top the agenda. The UK has a returns deal with Albania to speed up the deportation of migrants.

Mr Sunak said no issue required “Thatcher’s radicalism and drive” more than tackling migration.

As he praised the Italian prime minister, he said they were both “determined to break the business model” of these criminal gangs who traffic people in small boats.

The speech was delivered at a festival hosted by Ms Meloni’s populist Brothers of Italy party in Rome and bizarrely named after a character from the 1980s children’s fantasy film the Never Ending story.

To applause Mr Sunak told the crowd that if tackling illegal migration “requires us to update our laws and lead an international conversation to amend the post-war frameworks around asylum, we must do that.

“Because if we don’t fix this problem now, the boats will keep coming and more lives will be lost at sea.”

He added: “Our opponents just want to ignore this issue. They want to put their heads in the sand and hope it goes away. Well, let me tell them, it won’t.”

Mr Sunak said a lack of action would mean “our enemies will see how unable we are to deal with this and so will increasingly use migration as a weapon: deliberately driving people to our shores to try and destabilise our societies.”

Russia has already been accused by Finland of sending migrants to the European Union to destabilise the bloc.

Mr Sunak said: “If we do not tackle this problem, the numbers will only grow. It will overwhelm our countries, and our capacity to help those who need our help most.

“The costs of accommodating these people will anger our citizens, who won’t understand why their money should have to be spent on dealing with the consequences of this evil trade. It will destroy the public’s faith not just in us as politicians but in our very systems of government.”

Liberal Democrat Home Affairs spokesperson Alistair Carmichael acused Mr Sunak of using Ms Braverman’s “playbook”. He said: “Rishi Sunak is so desperate he’s reaching for the Braverman playbook, using divisive rhetoric to try to cover up his failures on asylum.Infighting within the Conservative Party is now generating a bidding war to see who can make the most toxic contribution to the debate.

“It is also a bit rich to say we need international cooperation when Conservative ministers are trashing the very treaties that we have signed up to deal with this. Who would want to cooperate with a government that is happy to disregard our legal obligations.Instead of posturing, Rishi Sunak would do better to focus on tackling the asylum backlog that is leaving people in limbo and costing taxpayers billions.” Earlier this year Ms Braverman, while she was still home secretary, used a widely disparaged speech in the US to warn that as many as 780 million people would be eligible to claim asylum without radical reform of global refugee rules.

She also faced a ferocious backlash after she singled out gay people to say “simply being gay, a woman or fearful of discrimination” was now effectively enough to qualify.