Pressed on whether this would be ended immediately, he said: “As soon as we can, but we will stop it.”

Sir Keir also said he would like to bring forward the 2029 deadline the Government has set to close all asylum hotels, saying: “I’m looking at alternative accommodation and doing everything we can to bring that forward.”

The Labour leader had earlier said he had “thought for some time that the left got it wrong” on immigration.

Asked when he realised this, he said: “Soon after I was a politician, I went to Oldham and met a number of people there who wanted to tell me what their concerns were.”

Speaking to Laura Kuenssberg on the BBC this morning at the start of Labour’s conference in Liverpool, Sir Keir said: “I’d like to bring that forward. We’ve got to process the claims, I’m looking at alternative accommodation and doing everything we can to bring that forward.”

Sir Keir said it was “not fair” that illegal immigrants could get taxpayers to fund £600 taxi journeys to GP appointments.

The Prime Minister insisted there are “too many examples” of people coming to the UK on student visas then claiming asylum.

He said: “We need to look at every aspect of illegal migration”.

Sir Keir said he has known for more than a decade that immigration in this country is not working.

Speaking to the BBC, he added: “I have thought for some time that the Left have got it wrong.”

It comes as Sir Keir said he believes Labour can “pull this round” as a poll suggested Nigel Farage could be on course for a landslide win in the next general election.

The Prime Minister hopes to use his party conference to unveil a series of eye-catching policies, including promises for the construction of new towns, with the aim of turning the tide for both Labour and his premiership.

But the scale of the challenge facing Sir Keir, who was swept to power with a massive majority just last year, was underlined by a poll indicating Mr Farage could be on course for Downing Street.

Labour’s conference in Liverpool begins on Sunday and Sir Keir said the battle against Reform UK and its “toxic” politics were “the fight of our times”.

The Prime Minister told The Sunday Times: “I think we can pull this round.”

But in a plea for party unity, after speculation Greater Manchester mayor Andy Burnham could seek a return to Westminster to oust him, Sir Keir said: “It is the fight of our times and we’ve all got to be in it together.

“We don’t have time for introspection, we don’t have time for navel-gazing. You’ll always get a bit of that at a Labour Party conference, but that is not going to solve the problems that face this country.”

A poll of nearly 20,000 people and modelling by More In Common suggested Mr Farage could enter No 10 with a majority of 96, with Labour reduced to just 90 seats and the Tories pushed into fourth place at Westminster behind the Liberal Democrats.