There are always exceptions. Since the nation voted to leave the European Union, the mayor of its capital city, Sadiq Khan, has declared that “London Is Open”, but he wouldn’t mind it being closed to Donald Trump. Hundreds of thousands of Londoners sympathise, judging by the map of signatories of the petition to stop the US president paying a state visit and making life difficult for the Queen.

This isn’t typical behaviour. In general, the capital welcomes foreigners, including those who, unlike Trump, plan to stick around and do something useful. About two million of the city’s work force of five million were born overseas, of which at least half come from elsewhere in the EU. London-haters find this frightening, a foretaste of foreignness eating the green and pleasant land. They hope Brexit will stem the alien tide, buttressing a fading Britannia of yore. They may not have yet grasped how damaging for them a cut in incomers from overseas could be.

Reducing foreign migration to the UK, the prime objective of Theresa May’s Brexit strategy, will have one of two impacts on London over time. It will either shrink the city’s vast economy or strengthen its pull on labour from elsewhere in the country. Neither would be ideal for those parts of the UK that voted most strongly to leave.

Facebook Twitter Pinterest London Is Open. Video: London mayor’s office

It’s not a great state of affairs, but the sobering fact remains that London subsidises the rest of the country. About 30% of UK taxes are generated from the capital, helping to fund health services and public transport and local authority functions all over England, Northern Ireland, Scotland and Wales. London depends on foreign workers to keep growing and therefore keep boosting that tax export. In a city desperate to increase housing supply, over a third of construction workers are foreign. In other sectors the percentage tops 50%, sometimes rising to close to 80%.

If Brexit shrinks the supply of such labour into London, either the subsidy stream out of London to will shrink too or London will compensate by seeking to recruit more workers from elsewhere, including other parts of the UK. Already, the capital is accused of sucking the life out of the rest of the country, as the young, adventurous and ambitious seek their fortunes in the capital. Other cities vacuum up the mobile and motivated too, but London is King Hoover. Should it choose to, it will attach its best internal migration nozzle and turn up the power. Is that what small town Brexiters want?

It’s to be hoped that those other cities and their surrounding areas will grow stronger in themselves and in relation to London. The introduction this spring of “metro mayors” to Greater Manchester, the West Midlands and the Liverpool city region should help them. It won’t help them, though, if London starts casting covetous eyes on their most talented and energetic people to counter a shortfall in foreign migrants caused by Brexit and, by the way, the government’s continuing pursuit of its elusive target of lowering the number of all foreign migrants to the tens of thousands per year.

Facebook Twitter Pinterest London is Open. Video: Transport for London.

There is, then, a strong case in the national interest for London to have its own post-Brexit EU migrant policy to allow the easiest possible recruitment of workers from those fellow European countries with which we will be no longer have a free movement agreement. Arguments for the creation of a London work visa or permit system that did not much need to exist until last June have since burst into the limelight. They have been taken up by Mayor Khan, the City of London, the London Chamber of Commerce and Industry and an all-party parliamentary group examining immigrant integration nationally, which argues for a full regionalisation of immigration policy, allowing different parts of the country to set its own, flexible rules and requirements. They’ve been explored by the London Assembly.

Such “asymmetric” arrangements already exist elsewhere, notably in Canada. They aren’t without their complications and are already meeting resistance from the usual suspects. The government, more worried about hardline Tory eurosceptics, its Ukip flank and the Brexit press than the official opposition, is unlikely to rush to embrace it. But Leave Nation is going to need Remain City. The UK’s future may now lie outside Europe but it is still very much in London’s hands.