Brexit has focussed attention – almost obsessively – on several ongoing dramas: on the negotiations between the UK and the EU; on the shifting balance of power within the Cabinet; and on the UK Parliament’s role in the process of leaving the EU.

But London and Brussels, where these stories play out, are only a part of the story. Britain’s decision to leave the EU is already unsettling and altering the nature of the United Kingdom itself.

Theresa May’s recent Mansion House speech put the dilemmas this creates front and centre. The Prime Minister argued that any Brexit deal must strengthen the union of nations. It must also, she insisted, benefit, and gain the support of, coastal towns and large cities with divergent views on the EU. Yet relatively little attention has been paid, however, to what this means in practice.

In a new report, a number of leading scholars have attempted to understand what Brexit might mean for the future of what Tony Travers neatly describes as “this unitary state with some devolved parts”. How will different parts of the UK be affected? And, where will powers and competences returned from the EU ultimately land?

These questions are crucial. After all, the Brexit vote has disturbed the devolution settlement. Politics in Northern Ireland have been roiled by the Brexit vote and its aftermath. The referendum triggered a (brief) revival of interest in a second Scottish independence referendum.

There was of course some discussion during the referendum campaign about the potential implications for the unity of the UK. In the weeks prior to the vote, for instance, Tony Blair and John Major, campaigning together in Northern Ireland, warned that a vote to Leave might have a destabilising effect not only in Stormont, but also in Scotland.

Subsequently, however, these debates have become more urgent. Discussions over the future relationship of Northern Ireland both with the Republic of Ireland and with the rest of the UK have of course featured prominently in press coverage of late. Brexit has fed directly into the sectarian divide, further disrupting a settlement already under pressure.

There is stalemate between London and Brussels on this. Brussels is anxious to secure agreement on a fall-back position under which Northern Ireland remains in the customs union and parts of the single market as part of the withdrawal agreement. The UK Government, for its part, wants the matter to be resolved as part of the trade talks.

And the issues are not confined to Ireland. Following the publication of the Withdrawal Bill, the Scottish First Minister Nicola Sturgeon accused the UK government of attempting a “naked power grab”. My colleague Roger Awan-Scully notes similar irritation in Wales. While the Welsh Government saw Brexit as a way of strengthening devolved powers, it too has come to focus on fighting a rear-guard action against what it sees as London’s attempt to snatch powers back for itself.

Last week, David Lidington set out how the UK government planned to address these criticisms while preserving the integrity of the UK’s own single market. The swift rejection of his arguments by the Welsh and Scottish governments bore eloquent testimony to the problems inherent in squaring the objectives of Westminster with those of Edinburgh, Cardiff and Stormont.

And all this is of immediate political relevance, given the Government’s need to secure legislative consent for the Withdrawal Bill and its reliance on the DUP. Solving the various Brexit-related dilemmas will require both ingenuity and trust. Both, however, seem to be in short supply at the moment.

Meanwhile, new political voices have joined the debate. The newly elected Mayor of Greater Manchester, Andy Burnham, claimed that Brexit should lead to greater devolution to cities and regions across the UK. Inequality, and the inability of London to provide adequately for the rest of the country, were, he argued, key drivers of the Brexit vote. Moreover, with the Westminster system “grinding to a halt” under the weight of Brexit, it was less able than ever to govern effectively. Tony Travers puts it somewhat differently, arguing that, with central government preoccupied with negotiating Brexit and trade deals around the world, devolution might offer an opportunity for the Government to lighten its load in order to focus on the primary task at hand.

Research from the Centre for Towns underlines how we are increasingly divided not only by nationality but also geography. Towns and cities are increasingly populated by different kinds of people, the former tending to be older and less well educated. This has increasingly translated into political divisions, as illustrated by the way areas that have experienced relative decline in recent decades voted Leave.

Meanwhile, Andrew Carter notes that, even were it not for Brexit, the economy would still face significant problems. Fifty out of 62 British cities lagged behind the national productivity average even in 2015. Leaving the EU will compound these problems, as cities are highly dependent on trade with the EU.

Yet, while the more vibrant cities will initially be the worst hit, Carter points out that they are also perhaps best placed to respond. Chloe Billing and others reinforce this point, arguing that those regions that voted Leave are more dependent on EU markets for their prosperity. The response, they argue, should be an industrial strategy that empowers cities. Yet, the Government’s instinctive reaction has been to centralise.

Leaving the European Union brings these socio-economic and constitutional issues into sharp focus. We need to be realistic about the fact that these are long-term problems, requiring long-term solutions. Yet they need immediate and sustained attention. Whatever the outcome of Brexit in terms of UK-EU relations, the UK must find a stable equilibrium for its own internal governance structures.