The extra figure is believed to run into the tens of millions of pounds, although the final sum has not been revealed by the Home Office.

Since 2015 the British taxpayer has handed over £124million to France.

Home Secretary Amber Rudd met her counterpart Gerard Collomb in London last week and French officials said that Ms Rudd was prepared to meet their demands for more money but there has been no new agreeement as yet.

Ministers are also said to be looking to renew the security contract surrounding operations at Eurotunnel terminals at Coquilles, Calais and Dunkirk.

This could cost around £80m, although the Home Office believes the figure could be lower.

Emmanuel Macron during his presidential campaign threatened to tear up the Le Touquet treaty, which permits British police to check and stop migrants in Calais.

However, Mr Macron’s administration now wants to reform the agreement with Britain paying for tighter security.

A Home Office spokesman said: “We work closely with the French authorities at all levels to reduce migrant pressures and target criminal gangs involved in people trafficking, both in northern France and further afield in source and transit countries.

“The Home Secretary’s meeting with the French Interior Minister last week is part of the ongoing dialogue to continue the work set out in the UK-France Declaration of 2015."

People-traffickers have recently started using a new tactic as a way to evade detection, a French official has said.

A “saturation” technique involves the traffickers sending up to six vans to a French port all at the same time in the hope that while one might get stopped, the others will make it to Britain.

Hundreds of refugees and migrants are believed to be living in the French port still, just over a year since the camp - known as the “Jungle” - was razed by police.

The region’s conservative mayor Natacha Bouchart claimed last month up to 1,000 migrants are sleeping rough on the city’s streets or in secret makeshift camps on the outskirts of town.

She said: “Between 800 and 1,000 people have returned to Calais. Migrants have decided, in an anarchic manner, that they have the right to be here. But don’t let them fool you – they are not helpless. Migrants know Calais better than anyone else. 

“They have smartphones and nice clothes. They’ve been told that they have rights, but no duties. 

"They drink themselves senseless – they down litres of vodka – and get into fights.”

Annabelle Sanderson, Brexit expert and former advisor to Nigel Farage who spent time in the camps of both Calais and Dunkirk said: "This additional cost to the UK tax payer to reimburse the French for their error in joining the Schengen Area is another unacceptable cost loaded onto tax payers by a government who thinks money grows on trees.

"The people I met in the jungle had travelled up through Europe and had not been stopped or remained in the first 'safe' country they arrived in because their ultimate destination was always going to be the UK.

"I met migrants from Iraq who told me they would not stay in France because only in the UK would they be given a house or free education. 

"If you remove borders to facilitate trade and movement then obviously illegal trade and smuggling will benefit too. France took this choice and the UK tax payer are once again being asked to pick up the bill.”