AMIENS, France/LONDON (Reuters) - France warned Britain on Thursday it would end border controls and let thousands of migrants move on to its neighbour if British voters backed leaving the European Union.

Migrants stand near a burning makeshift shelter set ablaze in protest against the partial dismantlement of the camp for migrants called the "Jungle", in Calais, France, March 3, 2016. REUTERS/Yves Herman

French Economy Minister Emmanuel Macron also said France would open its arms to British-based banks wanting to stay in the bloc, in comments published just before Prime Minister David Cameron met President Francois Hollande at an Anglo-French security summit.

Cameron has made protecting security a key argument in his campaign to keep Britain in the European Union in a referendum on June 23 and suggested last month that refugees living in a camp in the French town of Calais could flock to England if British voters decided to leave.

“The day this relationship unravels, migrants will no longer be in Calais,” Macron told the Financial Times, adding that rules allowing British-based banks to operate across the EU would be lost.

“Collective energy would be spent on unwinding existing links, not re-creating new ones,” he said.

After meeting Cameron in Amiens, 120 km (75 miles) north of Paris, Hollande also said there would be consequences for Britain if it left but did not want “to exert pressure on the British people”.

“There will be consequences in a lot of ways: for the single market, on financial markets, there will be consequences for the economic development between our countries,” Hollande told a news conference after the two leaders agreed to a 2 billion euro ($2.11 billion) drone-building project.

“I don’t want to paint a catastrophic picture, but there will be consequences including for people. It won’t call into question the historic, friendly relations between France and the United Kingdom. But it will have consequences including in terms of dealing with migration.”

SCARE TACTICS

Britain’s eurosceptics said the warnings were stage-managed, coordinated by the British government and part of a campaign of scare tactics to win the EU membership referendum.

Peter Bone, co-founder of “Out” campaign Grassroots Out, called Macron’s argument preposterous.

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“If asylum seekers start arriving at Dover, we will send them straight back. As an independent nation, outside of the EU, we will control our own borders whether the French government likes it or not,” he said in a statement.

But Cameron said it was nonsense to suggest the French warnings were part of a conspiracy by the “In” campaign.

“The best thing to do is to listen to the arguments ... and to understand some of the risks and some of the uncertainties about leaving the European Union,” he said at the summit commemorating the centenary of the Battle of the Somme in which 600,000 British and French soldiers died.

A British exit would rock the EU - already shaken by differences over migration and by fragility within the euro zone - by ripping away its second-largest economy, one of its top two military powers and by far its richest financial centre.

German Finance Minister Wolfgang Schaeuble said that Europe could become less stable if Britain leaves and that the bloc could also become less competitive.

Much of big business supports Britain staying in and according to a Reuters poll, foreign exchange strategists said Britain’s economy would be worse off if the country left. None of the 45 strategists polled by Reuters this week said the economy would benefit if the “Out” campaign wins.

Germany's BMW BMWG.DE wrote to its British employees about the risks of Brexit, as leaving is known, saying it was "much better to be sat at the table when regulations are set" rather than having to accept them.

The deputy managing director of Toyota Motor Manufacturing UK, Tony Walker, also told reporters that a decision to leave the EU would probably push up costs for Toyota in Britain and could raise questions about future investment decisions.

More than three-quarters of manufacturers and traders in Britain’s car industry believe that staying in the EU is best for business because of the risk of trade barriers and skill shortages if the country leaves, a poll showed on Thursday.

The British car industry body SMMT said 77 percent of its members said remaining in the EU was the best option, according to a survey conducted for the body by polling firm ComRes.

The prospect of leaving the EU also pushed growth in Britain’s dominant services sector to a near three-year low last month, according to an economic survey.

But opponents of EU membership, including Cameron’s main Conservative party rival, London Mayor Boris Johnson, said a vote to leave was Britain’s chance to break free.

“Let’s believe in ourselves again, rather than clutching the skirts of Brussels,” Johnson wrote in The Sun newspaper.