Late last year, the representatives of Britain’s overseas territories gathered in London. It is an annual event for these 14 appendices of empire, some of which, like Antarctica, are barely populated. Gibraltar, with its land border with Spain, is pre-eminent. Most of the others are small islands in hot places with a relaxed approach to tax affairs. In total, there are about 250,000 people living in these territories, who are protected by the crown and represented in their overseas dealings by the Westminster government.

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At the end of their deliberations the government issued a communique that comprised 20 paragraphs rehearsing the kind of problems that keep their leaders awake at night: their relationship with the UK, the impact of climate change, the consequences of natural disaster – and Brexit. The government pledged in the communique to secure the territories’ economic sustainability, and committed to ensuring that these interests were “fully reflected” in the UK’s negotiating position.

Manchester, Liverpool, Birmingham and Bristol could be forgiven for thinking it is time to move offshore. No such council exists for towns and cities across England. Whether they voted remain or leave, there is no forum in which the millions of voters of Greater Manchester, Birmingham, Bristol or Liverpool might be heard. There is no grand council in London where the people who fear for their jobs, who struggle to get by, who feel cut off from power, might be heard. There has been, so far, just one meeting between the northern mayors and the Brexit secretary, David Davis. Instead, the negotiations are conducted between the ideologues of the diehard Brexiter right and the bit of the Tory party that is still in touch with the reality of leaving.

There is no excuse for treating the future of the UK as a matter of internal Tory party politics. The constitutional crisis that leaving the EU will provoke for Northern Ireland and Scotland’s relationship with the rest of the UK is already painfully clear. There is no obvious solution to their grievances, but at least they are part of the dialogue. The consequences for the voters who made leave happen, the voters of non-metropolitan England, are ignored.

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Yet only last year, the map of the Brexit vote was overlaid with a whole new voice for the regions. For the first time, the west of England, Greater Manchester, Liverpool, Tees Valley, the West Midlands, and Cambridgeshire and Peterborough – most of them places with an inner core of remain voters and a larger outer ring of leavers – all elected their own mayor. Each metro mayor reflects, more or less perfectly, the English attitude to Europe. These surely are the voices that belong at the heart of the negotiations.

Boris Johnson warns that reversing the referendum result would be a betrayal. But if Brexit fails to be the panacea for the ills that trouble its supporters, the betrayal will be as great. Political pragmatism alone makes it vital that angry, disenchanted Brexit voters feel that what comes next is going to assuage their grievances. They were promised they would be in control.

It is very difficult to see why they should feel as if the promise has been honoured if they continue to live in a country where decisions that affect their daily lives are taken hundreds of miles away. Where the local hospital is floundering because there are no skilled EU workers, yet thanks to the education system, they lack the skills to take the vacant jobs. And where the local economy is tanking and the international students who kept it frothing – to the tune of £2bn in the north-west and the West Midlands, and another billion each in the south-west and the north-east – have disappeared, sacrificed to immigration quotas.

For the metro mayors, this is a particular kind of nightmare. On the one hand, they are in political utopia, elected to create a new democratic entity that has enough scale to deliver skills, jobs and economic regeneration, and to transform lives by tackling childhood disadvantage and rotten housing. On the other, they struggle for the power and the revenue that can make it happen.

Theresa May needs a way through Tory wars. Listening to the voice of the regions would be a handy place to start

Every study into the impact of leaving the EU comes to the same conclusion: it will hit hardest the areas that most hoped Brexit would be a way out of their problems . So far, research suggests London and the City will survive relatively unscathed. The thinktank IPPR North reckons the north of England will be hit twice as hard. It found northern regions were 50% to 60% more dependent on EU trade than those in the south. The government’s own analysis is as bleak.

It is not much more than a year since the metro mayors were campaigning on party tickets. Now they find themselves united in pragmatic defence of their local economies against a power-hoarding, Brexit-focused centre in London. Andy Street, the Conservative mayor of the West Midlands, sounds as fed up as Manchester’s Labour mayor, Andy Burnham, about Westminster’s failure to deliver them the power they promised over the skills budget, which will delay efforts to start building a post-Brexit workforce. Burnham warns that local employers are anticipating a “massive issue” with recruiting and retaining staff. All the mayors want to keep control of the EU structural and investment funds that are vital for their economies. All of them know that they have a year – or perhaps two – to make a difference, and that without their input, Brexit is likely to blow them out of the water.

But Westminster isn’t listening. Last week, Theresa May went to Manchester to make a big speech. The only problem was that it was on the 60th anniversary of the Manchester air disaster, which wiped out the heart of Manchester United’s young squad when the plane crashed after a refuelling stop in Munich. Downing Street apparently didn’t know.

This week, a study by an academic group, The UK in a Changing Europe, found levels of pessimism and powerlessness in England’s provincial towns and cities almost unchanged since the Brexit vote. Out of London and the south-east, away from the burgeoning night economies of Bristol or Leeds or Manchester, in the stoical provincial territory where Brexit is an article of faith, they still feel distant and invisible.

A new form of local government is an improbable miracle cure. But the mayors have a mandate of admirable simplicity: to make their region a better place to live by bringing people together and working beyond ideology. Theresa May needs a way through Tory wars. Listening to the voice of the regions would be a handy place to start.

• Anne Perkins is a Guardian columnist and leader writer