Just over the road from the Tower of London lies a stretch of wall some 10 metres high and 2,000 years old. It is all that remains of the London Wall, a 4km-long structure that wrapped around the city that the Romans called Londinium. For the Romans, building a wall around a city was a sensible move – a way to protect it from enemies real and imagined.

Two millennia later, the idea of building a wall – closing the borders – would be anathema to most Londoners. This is a city that has thrived on immigration, a city whose heart beats to the rhythm of hundreds of different languages. Like no other city in Europe, let alone in the UK, this is a truly global metropolis. For Londoners, immigrants aren’t a menace; they are our friends, family and colleagues. Without them the city is finished. And yet, following the UK’s vote to leave the EU – a decision that Londoners opposed by 60 per cent to 40 per cent – this openness is no longer guaranteed.

The promise of the Leave campaign to “control” immigration can be interpreted only as a vow to reduce it: the 1.7 million Londoners who were born in other EU countries do not know for sure if they will be allowed to stay; the flow of newcomers will almost certainly be curbed. Businesses across the city worry that they will no longer be able to compete for the best and the brightest from around the world. There are implications for theatres and cafés, for care homes and schools, for hospitals and transport. Reduce the pool of foreign labour and London grinds to a halt.

Right now there is little that London can do to stop this. Its mayor, Sadiq Khan, has limited powers. He does not control the education system like his counterpart in New York; nor does he have control over much of the city’s tax take like his opposite number in Tokyo. He certainly has no say over immigration.

In the weeks following the referendum more than 200,000 Londoners have signed a petition calling for the city’s independence. The petition is both a joke and a howl of frustration. London will not break away from the UK. But while full independence is not on the table, greater autonomy is possible. Can London be both a global city and a national capital? Could London become a city-state within a federal Britain?

“It’s almost inevitable that London will demand or seek greater autonomy from the rest of the UK,” says Tony Travers, a professor of local government at the London School of Economics. “London is a very different space with very different public-spending priorities and a different view of the world. The argument for a more autonomous position within the UK is a powerful one.”

Initially, autonomy will be sought for tax and spending. “We don’t have the powers that cities such as Tokyo, Paris and New York take for granted,” says Ben Rogers, director of the Centre for London. Those cities are able to raise their own taxes on a far greater scale. As a result the UK capital has to rely on central government for two thirds of its income, while New York leans on Washington for just 30 per cent and Tokyo takes as little as 7.7 per cent of its income from the Japanese government.

“If we had more control over our property taxes we could design a tax regime that is good for both the London economy and the country,” says Rogers. “You could redesign council tax so that it discourages under occupation. You could have a land levy tax that means you pay tax on the value of the land regardless of what’s built on it, which would encourage people to develop their land.”

None of this solves the big problem: London would prefer to stay in the EU, happily accepting freedom of movement in return for full access to the single market. Whereas other parts of the UK appear to see freedom of movement as the price, for London it is the prize. Could a more powerful London introduce its own immigration regime? It’s unlikely but it’s not impossible. Canada has a provincial element to its immigration programme – new arrivals are given visas for specific provinces – and Australia has its Regional Sponsored Migration Scheme, which enables towns and regions with skills shortages to apply for permits for newcomers.

Rohan Silva, a former adviser to David Cameron and George Osborne, believes it would be possible. “You could give London the power to create its own work visas,” he says. “The primary place of residence would need to be in London. It would be politically possible and the London public would be in favour.”

Travers believes it could work too. “Let’s say the government wants to reduce net migration to the UK. But London, led by the mayor, says it wants to continue to have immigration at the level it had before. Can London bid for more migration? Would that be acceptable? I don’t see why not.” There is little risk that migrants who are given permission to move to London will decide to move elsewhere. And given that international workers have to provide their passport details to their employers it would be impossible for them to get a formal job in another part of the country.

“Ultimately,” says Silva, “London is screwed if it’s not open to the brightest investment around the world. We’re at real risk of becoming more closed unless we fight for a more sensible modern approach. No one else in the country is going to care enough to do it.”

A London with greater tax and spending powers, with control over education and healthcare and with its own liberal immigration policy, would start to feel very different from the rest of the UK. But according to Nicholas Walton, breaking away and becoming a city-state would be a disaster for London.

Walton lives in Singapore and is writing a history of city-states; he is also the author of a book on one of the originals, Genoa. “The world is a different place from when certain city-states were particularly vibrant,” he says, adding that the only places that make a success of it now are those with “strange tax policies or petrochemicals”. Or they are places such as Singapore, which succeeded thanks to the autocratic leadership of Lee Kuan Yew. “He could hammer the country through force and belligerence. London can’t do that; it doesn’t have someone directing things.”

London, Walton argues, is too intertwined with the rest of the UK to go it alone. “This idea that London stands apart from the rest of the country is completely wrong. If you cut off the blood supply, things wither and die. It would be a massive case of hubris.”

After London and its nine million inhabitants, the next largest city is Birmingham with one million. While in Germany the major industries are spread across the country, in the UK almost everything of note is based in London. This has a knock-on effect on public services: as graduates tend to marry fellow graduates, the best teachers and doctors also tend to end up in London. The capital now has better exam results than any other part of the country.

The divide between London and the rest of the country was one of the big issues that arose from the poisonous Brexit debate. “Big cities and their relations to their nations is an interesting issue,” says Rogers. “You see it in New York and in Paris too but it’s a particular problem in the UK because London is not just the economic capital, it’s the cultural capital and the political capital – it’s the capital of everything.”

In calling for greater powers, London needs to ensure it doesn’t forget that it is also the UK’s capital. “London is extremely bad at selling itself to the rest of the country,” says Rogers. “We never stop talking about ourselves as a global capital whereas we rarely talk about ourselves as a national capital. It’s not surprising that people feel fed up.”

London’s best hope is to join the broader conversation about the kind of country the UK wants to be. Scotland may have rejected independence in 2014 but the Brexit result has put it back on the table. In northern England, Greater Manchester and Merseyside are about to receive more power. If ever there was a moment for the UK to consider whether it should become a federal state, this is it. But Silva doesn’t think it’s likely: “A piecemeal way is the British way; we don’t go in for grand theories and revolutions.”

He may be right. The UK has never had a constitution and right now, in an age where experts are ignored and politicians treated with scorn, the likelihood of any Royal Commission into federalism being a success is slim. London will not become a new Singapore, nor will it take inspiration from the great Italian city states of the early second millennium. It will not be a tax haven like Monaco, nor will it ride a wave of nationalist sentiment like Barcelona and Catalonia.

Most importantly, London’s desire for autonomy will not be driven by nationalism. If the UK capital gains more autonomy – if it one day becomes a city-state within a federal nation state – it will create something unique. It will be arguably the first time in history that a region has sought greater power in order for outsiders to have more influence, not less.