In a distant echo of a medieval monarch’s royal progress around the realm, Boris Johnson has been journeying on a prime ministerial grand tour around the country to show his new subjects who is boss. Last weekend it was northern England; on Monday, Scotland; Tuesday was Wales day and Wednesday was the turn of Northern Ireland.

These visits contained none of the celebratory pageants that would have been expected in the middle ages. Instead, the new leader was whisked in and then out again. Much of the tour has been controlled. Journalists were mostly kept at a distance. In the streets, boos seem to have been more common than cheers.

It is hard to dispute the widening gulf between current reality and the rhetoric of Johnson’s ‘awesome foursome'

Like Theresa May did, Johnson talks the talk about holding the United Kingdom together amid the disruption of Brexit. He has even cast himself as minister for the union. But it is hard to dispute the widening gulf between current reality and the rhetoric of both May’s “precious union” and Johnson’s “awesome foursome”. Tours like Johnson’s only emphasise that this union is increasingly divided – and perhaps even breaking apart.

Politically, by far the most urgent stop on Johnson’s tour was in Northern Ireland. The most fraught of the visits was probably the one to Scotland. But in many ways the most telling trip was Johnson’s foray into Wales on Tuesday, when he cuddled a chicken in Newport, visited a retail company in Brecon and met Wales’s Labour first minister, Mark Drakeford, in Cardiff before heading to Belfast.

Wales was not included in the Johnsonian progress merely for completeness’s sake. It was also there because of Thursday’s byelection in the vast and lovely mid-Wales rural constituency of Brecon and Radnorshire. The result will test whether there is the Johnson bounce for the Tory party that his supporters crave, or whether Jo Swinson will be celebrating a Liberal Democrat recapture of a seat that the old Liberal party first won in a famous 1985 byelection.

Yet Wales should never be overlooked. In discussions about the UK’s constitutional and political distresses, Wales is all too often treated as an afterthought. The reasons are not hard to see. Modern Wales has endured little of the existential pain of Northern Ireland. The nationalist cause has never carved through Welsh politics the way it has in Scotland. Wales has been welded to England for far longer than the other nations. And its support for devolution was often lukewarm.

Yet amid the more eye-catching convulsions of Brexit elsewhere, the old idea that nothing is likely to change in the relationship between Wales and England is looking lazy. That’s not to say that Welsh independence is on the cards any time soon. But it most definitely is to say that support for Welsh independence is liable to rise, and possibly to rise quite fast if Brexit eventually triggers either Irish reunification or Scottish independence, let alone both.

Johnson’s personality contributes its own flame-thrower to this combustible mix. His insouciance this week about the devastation that threatens the Welsh hill-farming industry from a no-deal Brexit could come back to haunt him, and not just on the sheep-farms of Brecon and Radnorshire. The land, like the language, plays a dynamic role in nationalist consciousness. Angry farmers can make a leader suddenly vulnerable. Look what they and the “gilets jaunes” did to Emmanuel Macron.

But this volatility is not simply about Johnson’s Marmite personality. Nor is it simply about the single-mindedness of the nationalist parties to exploit every situation for the separatist cause. It is also structurally bound up with Brexit itself, whatever the terms.

In a lecture in June, the civil servant formerly in charge of the Brexit department, Philip Rycroft, laid this on the line. “The fact of Brexit poses a series of challenges at a practical, as well as an existential, level to the current governance of the United Kingdom,” Rycroft said. “It seems clear that this and any future UK government is going to have to devote considerable time and effort to reworking its policy towards the union.” He concluded: “Our sense of social cohesion, indeed the very cohesion of the United Kingdom, will depend on it.”

Rycroft offered some well-chosen illustrations. What if Scotland chooses to subsidise its fishing fleets while England does not? What if Welsh hill-farmers secure a differential subsidy rate for their lamb that northern English hill-farmers cannot access? “The requirement for increased agreement across a whole range of new territory increases the scope for friction,” he concludes. “It will put new pressure on a system of inter-governmental relations that was devised for a very different era,” he suggests.

It is important not to exaggerate, of course. There are many bridges to be crossed before Wales becomes as much of a threat to the union as Northern Ireland and Scotland now are. There are radical ways of heading off the disintegration of the United Kingdom, including the federalist new Act of Union proposed by Lord Lisvane and extolled by one of the prime minister’s former colleagues in the Daily Telegraph this week. But Brexit has put the possibility of breakup squarely on the table, even in Wales.

Outright support for independence in Wales languishes in single figures. But more than one in three Welsh voters now feel some support for the idea, and the proportion of those whom nationalists dub the “indycurious” is clearly rising. Use of the Welsh language is growing and becoming more fashionable. Even Drakeford said in July that his support for the UK was not “unconditional” and that, if other parts seceded, it would be sensible “to reassess Wales’s place in the components that were there in the future”.

Wales is no exception to the disruption of old ideas that Brexit is causing. Only this week, Plaid Cymru came first for the first time in a Welsh Assembly voting intention poll . There are many differences, but the overturning of the old order that occurred in Scotland a generation ago could now be starting to repeat itself in Wales too. Labour has never been weaker, and Jeremy Corbyn refuses to engage on these identity issues. But it is a big stretch to say that Labour’s decline means Wales will soon be pressing for or achieving independence. Five hundred years of union are unlikely to dissolve in a hurry. Yet modern politics is nothing if not volatile. Wales’s sense of nationhood takes many forms and has gone through many changes, but its existence as a living reality is undeniable.

Around the time of the last Brecon and Radnor byelection, the lateand life-enhancing Welsh historian Gwyn Alf Williams wrote about the continuing potency of the legend of Owain Glyndŵr. “Since 1410 most Welsh people most of the time have abandoned any sort of independence as unthinkable,” wrote Williams. “But since 1410 most Welsh people, at some time or another, if only in some secret corner of the mind, have been ‘out with Owain and his barefoot scrubs’. For the Welsh mind is still haunted by its lightning-flash vision of a people that was free.”

Boris Johnson would be wise to remember that thought. If he does not, he may even turn out to have done more for Welsh independence than almost anyone since Glyndŵr himself.

• Martin Kettle is a Guardian columnist