Mr Johnson’s letter had five proposals, which included officials from both countries joining forces to patrol French beaches and a “returns” agreement for France to take back migrants who reach English shores by boat.

It was the latter proposal – which effectively replicates a deal the UK had while in the EU – that appeared to especially anger Mr Macron’s team, as well as the manner in which the letter became public.

Mr Macron said: “I am surprised by methods when they are not serious. One leader does not communicate with another on these questions on Twitter, by public letter.”

Gabriel Attal, the French government spokesman, said during a television interview about the letter: “We are fed up with double-talk,” adding that it was “both poor in substance and totally inappropriate in style”.

Mr Attal also said: “We are fed up with the way they are externalising problems. You wonder whether Boris Johnson doesn’t regret leaving Europe because whenever there is a problem, he considers that Europe must handle it. But that is not the way it works.”

Returns agreement similar to Dublin Regulation

At the heart of some of the criticism from France was the suggestion that the UK had chosen Brexit with a promise to “take back control” of its borders, but was now trying to readopt an EU measure it had left behind.

While in the EU, the UK had benefited from the Dublin Regulation, which dictates that an asylum seeker should normally have their application processed in the first EU country they arrived in. It meant, theoretically, that someone seeking asylum would be returned back to that country if they moved to another EU nation.

Mr Johnson’s suggestion that a bilateral “returns agreement” should be signed with France, whereby migrants who arrive on UK shores after crossing the Channel should be returned to France, is seen by critics as an attempt to establish a version of the Dublin Regulation.

Pierre-Henri Dumont, Calais MP, said he was “surprised” by the Prime Minister’s demand for a returns agreement with France.

He said: “What we are facing right now is an aftermath of Brexit. The UK left the Dublin agreement.

“So it’s a bit strange that the one who pushed for Brexit is now asking for something that was contained with membership of the EU.”

Michel Barnier, the former Brexit negotiator for the European Commission, said: “It is obviously an additional provocation of Boris Johnson. He is in a state of mind of confrontations on all subjects with the EU.

“This very serious question deserves much better treatment than controversy and confrontations.”

But a Home Office source argued that the Dublin Regulation was never working as intended while the UK was in the EU.

“Dublin didn’t work. It doesn’t work for France, it didn’t work for us, it doesn’t work for countries across Europe. So actually I don’t think that’s a fair criticism,” the source said.