Theresa May cannot say she has not been warned. Brexit poses a mounting threat to the unity of the UK. Nor can she dispute the eminence of those who have been doing the warning. During the referendum campaign in 2016, John Major counselled that a British exit could “tear apart” the UK. This past summer, Gordon Brown argued Britain was at serious risk of “being permanently paralysed by seemingly irreparable divisions”. These are serious voices.

To the unwary, their warnings might seem to have been directed at receptive ears. Few serving prime ministers express their commitment to the union more often or more clearly than May. She calls it her “beloved union”. Last week, at her party conference, she called it her “precious union”. It would be wrong to doubt the sincerity of such words. But the impact of Brexit on the union is now more threatening than ever, and May seems to possess a wholly inadequate armoury of words, ideas and actions to mitigate or prevent it.

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When May talked about the union in Birmingham, it was clear from the context that she was thinking primarily about the union with Northern Ireland. Given that the Irish border is, by her own admission, the crunch issue at stake in the Brexit negotiations, this is hardly a surprise. What is more surprising is that, as a supporter of the union, she has been so obtuse about accepting the political consequences of what needs to be done.

The obvious union-defending solution in Ireland has always been for the UK to remain in the EU customs union. It still is. This may yet be in the package that may emerge later this month. And there would be a majority for it in parliament if she took that course. Yet the union is clearly not quite precious enough for May to take that step.

If anything, May has been even more churlish in her handling of the union with Scotland. In her relations with Nicola Sturgeon’s Scottish government, she has been an uncompromising centraliser. Scotland’s 62% vote for remain has been consistently ignored. So have Sturgeon’s various ideas – some of which were moderate and reasonable – about mitigating Brexit in Scotland. Instead, some Scottish devolution powers have been suspended and the UK government has fought a court case against the Scots: a curiously tough form of love.

To be fair to May, dealing with this Scottish government is not easy. The SNP wants out of the union altogether. It uses any and every issue to leverage the case for separation. To make a Brexit deal with a party trying to use Brexit to advance the separatist cause would test even a skilful negotiator, which May is not.

Nevertheless, Sturgeon made a telling point on Tuesday when she compared the receptivity of the EU to Ireland’s special concerns in the Brexit negotiations with the hostility of the UK government to the special concerns of Scotland. May has been unbending towards a part of the UK that – never forget – voted decisively in 2016 to remain in the EU. The result, as Brown put it in June, is that there will be “long-term consequences” from May’s approach. And those consequences directly threaten the stability of the UK.

The post-Brexit horizon might not be so dark if May possessed more emotional intelligence and more inclusive political skills when she addresses both Ireland and Scotland. Those are skills Ruth Davidson possesses in abundance, and not just because she is a Scot. But May is not one of those politicians who have the skill to give themselves elbow room. And, in fact, the problem is worse than that.

May’s approach to Brexit has never had space for compromise with the 48% of the UK that voted remain. But she has consistently made compromises with a section of the Tory party that cultivates a particularly reactionary form of Anglo-Britishness, and which regards Brexit as much more important than the preservation of the union. Polling this week showed that 77% of English Tory members would rather see Scottish independence than abandon Brexit; much the same proportion of May’s party say they would sacrifice the Irish peace process too.

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These are the people and the political culture by which May’s Brexit approach is now inextricably compromised. In addition to spurning Scottish concerns (not just nationalist ones) and as well as cleaving to the DUP’s very one-sided view of British-Irish relations, May’s approach to Brexit has empowered a deeply partisan version of Englishness. This has political consequences that will come back to haunt the country, perhaps very soon. They would deepen and darken if Boris Johnson were to replace her.

It is possible, perhaps even probable, that a fudged and messy Brexit will stop these issues from coming to a head for a while. But a lot of damage has been done and it goes on being done. The problems existed before Brexit – Scotland came very close to separating from the UK long before the EU vote – but Brexit has intensified them because is has given such a boost to a reactionary form of Englishness.

There is no simple answer to the crisis of the United Kingdom. But no answer will suffice that does not, as Sturgeon put it this week, embrace “real partnership”. This week, an enlightened group of peers from all parties will launch a new Act of Union Bill, which would reimagine the UK’s constitutional arrangements on the basis of respect and partnership between the component nations and a desire to make a form of federalism in these islands work.

The bill will not get far, initially. It nevertheless sets a far more progressive direction of constitutional travel than May offers for those of us who wish to preserve the union and not to break it up. But much direct damage has been done by Brexit, and it may be too late.

• Martin Kettle is a Guardian columnist