Theresa May has rightly read the Brexit vote as a popular revolt against metropolitan trendies like David Cameron and Jeremy Corbyn and every other variant of the species. Given the chance to poke the whole pack of us in the eye, what with our “progressive” values and smug, big city ways, Leavers seized it with Faragist glee. The prime minister has taken their cue. Disastrous, disordered and unlovely it may be, but her Brexit stance has, at least for now, caught the mood and achieved the substantial feat of making the Labour leader and his coterie look even more clueless than they did already.

But May presumably also knows that the path she’s set could lead to economic calamity. For now, she can afford a bit of that: prosperous Outers may be ready to be a little worse off for a while in return for their hoped-for reassertion of their idea of their country’s true identity; the less prosperous who voted Leave, many of whom don’t normally vote at all, have low expectations about everything anyway. Even so, May won’t want to preside over too steep or too ugly a decline. With Keir Starmer on the case, even Her Majesty’s Opposition might help make something useful out of it. That is why May badly needs the very things the Brexit vibe she’s milking most reviles.

London, like it or not - and this is hardly ideal - is the key to UK financial health. Globalised, multicultured and full of immigrants, it powered through the last recession as the rest of proud Britannia flailed. At the last count, London was generating £364bn of the UK’s £1,590bn annual economic output – a massive 23% of it, with the surrounding south east of England contributing a further 15%.

Between 2010 and 2014, London’s economy grew by 6.8% compared with 4.4% for the UK as a whole. London’s workers’ output is 73% above the average. When Brexit darling Boris Johnson wrote three years ago that “we can no longer blame Brussels” for our problems and should look instead at our own “sloth” – especially when compared with “the Germans” – he might have named the labour force of the city he (loosely-speaking) led as mayor at the time as an exception.

Britons who fear and loathe London and all it symbolises in their eyes might note that taxes raised in the capital help fund their public transport, their affordable housing, their health services, their schools, their police officers and the upkeep of their public footpaths and parks. Almost one third of UK taxes are raised in London. A report compiled for Johnson found that the equivalent of £2,500 per Londoner subsides the rest of the UK every year.

So here’s an irony: even as the PM endorses the disruption of all that is integral to the nation’s capital – its international business links, its receptiveness to foreign incomers, its resulting cultural variety - she is to draw more deeply from its well of wealth. A revaluation of business rates looks set to increase London’s tax bill by an average of 11% - amounting to more than £700m - while in most of the rest of England rates will go down.

Johnson’s successor at City Hall, Sadiq Khan, has called this a “kick in the teeth” for the capital. The London Chamber of Commerce and Industry has warned of the dangers of London business being seen as a cash cow. The Institute for Fiscal Studies comments from a wider angle: “It will contribute to the ongoing trend of the UK government becoming more and more dependent on revenue from London to fund services across the whole”.

Here is the intensifying context for the continuing debates about giving London government and those of other big city regions greater autonomy. No one is demanding a bigger piece of the pie, just more control over the piece they have. Regional, rather than Whitehall, decisions about transport infrastructure, housing, schools and skills training should mean better results, with social and economic gains to follow.

Progress in that direction had already been made in the form of new, executive “metro” mayoralties for Greater Manchester, the Liverpool city region and the West Midlands. Inaugural elections will take place next year. The victors will be looking for more powers to be sent their way. In London, Khan is pressing for post-Brexit arrangements that will help the capital, which voted 60-40 to Remain, to maintain its status as a city that is “open for business”, including the creation of a London-only work visa.

Some of his critics, still truffling for imagined un-Britishness in the born-and-bred Tooting boy, imply that in so doing he seeks to subvert the national will. Well London, didn’t want what “Good old Boris” helped them get, and other big cities felt much the same way. They are the very parts of Britain the prime minister must help to better help themselves if Britain is to survive her Brexit strategy. She needs London. She’d be wise to give the capital what it needs too.

Dave Hill is the author of Zac versus Sadiq: the Fight to Become London Mayor, available from the Guardian Bookshop.