Parisian officials have reportedly rejected the offer, fearing that it represents a violation of French sovereignty. It comes as Home Secretary Priti Patel has confirmed ongoing talks on possible joint Franco-British maritime patrols in the Channel.
The number of migrants crossing the Channel reached a record 4,019 this month, surpassing the previous record of 3,879 in September.
Only five of the more than 25,000 asylum seekers who made the perilous crossing this year have been returned.
Asked about possible joint patrols in the House of Commons, Ms Patel said: “We are discussing all options, whether it be naval patrols or alternative patrols. “
She added: “It is not appropriate for me to comment on the responsibilities of other departments on this matter, but work is underway with our counterparts and with other government departments. “
Priti Patel on the brink: No10 loses confidence as Channel crossings increase
Meanwhile, senior conservatives warned on Monday that a failure to tackle the record number of migrants crossing the Channel could fuel the rise of a new UKIP-style political party.
Nick Thomas-Symonds, Home Secretary for Shadow Labor, accused Ms Patel of “empty rhetoric” about her failure to address the issue.
The Home Secretary hit back at his attack, insisting the Tories have a long-term plan to tackle immigration.
Former Brexit Secretary Stephen Barclay, Chancellor of the Duchy of Lancaster, has been tasked with the review.
The Prime Minister was grilled on the subject when he appeared before the 1922 Conservative MPs Committee last week.
Former Cabinet Minister Sir Iain Duncan Smith reportedly challenged Mr Johnson at the meeting, telling the PM: ‘Migration was in our manifesto, it was in our DNA. If we don’t, they won’t forgive us.
His remarks were reportedly greeted with a slam of desks in support from his backbench colleagues.
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This summer, the Home Secretary agreed to pay France £ 54million for helping to block level crossings.
The first installments of the payment have already been paid to Paris by London.
In the past three months, France has stopped 65% of attempts at crossings by illegal immigrants, against 50%, said Gerald Darmanin, the Minister of the Interior.
On a practical level, Mr. Darmanin declared that he had received the assurance of increased surveillance of the coastal zone, in particular by aerial surveillance.
However, the feud between France and the UK is also about post-Brexit politics and fallout.
Mr. Darmanin called for the opening of negotiations for a migration treaty between the European Union and Great Britain.
He said: “We have to negotiate a treaty since Mr Barnier did not do so when he negotiated Brexit, which binds us on migration issues”.