Back in January, the prime minister promised he would "pass new laws to stop small boats, making sure that if you come to this country illegally, you are detained and swiftly removed".

But over 29,000 people have made the dangerous journey since - the second highest annual figure on record - the government's plan to deport asylum seekers to Rwanda has been ruled unlawful, and a bill to address judges' concerns is causing a rift in the Conservative Party.

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Facing questions from parliament's Liaison Committee, Mr Sunak insisted "considerable progress" had been made, with the number of arrivals down by 30% this year.

But, he told the cross-party group of MPs: "There isn't a firm date on this because I've always been clear from the beginning."

The prime minister added: "We will keep going until we [stop the boats]. This isn't one of these things when there's a precise date [or] estimate on it.

"This is something where before I took this job they had only ever gone up, now they're down by a third."

During the 90-minute grilling by various Commons committee chairs, Mr Sunak also appeared to admit there were no companies willing to provide the flights to take asylum seekers to Rwanda, even if the contentious bill allays the fears of the Supreme Court - and manages to get through parliament.

The story was first reported by the Times over the weekend, saying airlines had refused to sign contracts with the Home Office over fears of "reputational damage".

Mr Sunak said he was "confident" the government could get asylum seekers sent to the African nation despite the reports.

Asked whether the government had any airlines on board, he said: "You wouldn't expect me to comment on commercial conversations that are necessarily private but I'm highly confident that we can operationalise the [Rwanda] Bill in all its aspects."

The prime minister also got into a spat with Labour's Dame Meg Hillier over how much more would be poured into the Rwanda scheme.

It was revealed this month that the cost of the plan so far had hit £240m, despite never being used, and that an extra £50m would be paid to the country's government within the next year.

Dame Meg, who chairs the Public Accounts Committee, pushed Mr Sunak about how much more the scheme could cost, attacking the "secrecy" around the payments.

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But the prime minister refused to give any more detail, saying: "It may well be that we want to have other conversations with other countries.

"It wouldn't be right to talk about these things if we're having private conversations with other countries about potential alternatives to add to our Rwanda policy."