Yvette Cooper, the shadow home secretary, told Sky News the remarks were "clearly wrong" and that instead of promoting division, ministers "should be getting on with sorting the problems out".

Tory deputy chairman Mr Anderson made the comment about asylum seekers after it emerged about 20 of them were granted a last-minute reprieve from boarding the Bibby Stockholm accommodation vessel on Monday.

His use of the F-word has been backed by Downing Street and several senior Tories, who said he was expressing the frustration of the British public.

Asked if that is an appropriate phase for a politician to use, Ms Cooper said: "No, it's clearly wrong. And this is ramping the rhetoric to distract from the fact that the government is failing.

"Instead of promoting division, what they should be doing is getting on with sorting the problems out. Rishi Sunak's plan is just not working."

Ms Cooper said despite repeated pledges from the government to "stop the boats", the number of Channel crossings in June and July this year were higher than last summer and there are also 10,000 more people in hotels.

Citing Labour's plan - which includes scrapping the Rwanda deportation scheme and funding a cross-border police unit - Ms Cooper said: "What we need to do is go properly after the criminal gangs that are making huge amounts of money from the dangerous boat crossings and also clear the asylum backlog.

"That's what Labour would do. We've set out a new fast track system to do that so we can end hotel use, the barges, the [military] bases, all of that and get back to a proper functioning system."

Labour has been seeking to hammer the government on immigration failures - particularly the backlog in the asylum system - amid accusations from Tory MPs that "leftie lawyers" linked to Labour are sabotaging the government's small boats plan.

On Tuesday, shadow transport secretary Louise Haigh told Sky News it was "nothing short of risible" to suggest an opposition party that has been out of power for 13 years can be blamed for the current problems.

On Monday, just 15 migrants entered the Bibby Stockholm following legal challenges to stop others moving on to it.

The floating accommodation off the Dorset coast is one of several sites being used to reduce reliance on expensive hotels - but transferring migrants to the vessel has been mired in difficulty and delays amid safety concerns and local opposition.

The barge will ultimately house 500 single men - but that is less than 1% of the 170,000 people waiting for their claims to be processed and Labour says it is currently being used in addition to hotels, not instead of.

Mr Anderson admitted on Tuesday the government had "failed" on immigration as he stood by his comments.

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He said his use of the F-word was "born out of frustration" at those objecting to go on to the barge, and he would not be apologising.

But asked if the Conservative government had failed to tackle illegal immigration effectively, Mr Anderson told GB News: "We have failed on this, there's no doubt about it."

UK 'has most comprehensive plan in Europe'

However, immigration minister Robert Jenrick said he did not agree with those remarks - even as he backed Mr Anderson's "f*** off" comment.

He told Sky News: "Lee was expressing was the deep frustration of the British public, not just the numbers of people crossing the Channel, but the apparent refusal of some people to accept perfectly decent accommodation."

However, asked if Mr Anderson was speaking for the public when he claimed the government's policy was failing, Mr Jenrick said: "I don't agree with that."

He said a returns agreement with Albania had led to a 90% drop in people coming from the southern European country, while deals with France have helped intercept migrants on beaches and a new partnership with Turkey has just been announced to crack down on people smuggling gangs.

"And so on each and every front, we are working intensively," he said. "And I genuinely believe that the UK has the most comprehensive plan of any European country to tackle this issue. "