After a year of unprecedented political change, it’s worth thinking about all the things that haven’t changed. Voters in Britain and America may have upended the political order with their choices at the ballot box, but the systems that produced these results have been left more or less untouched.

This is most stark in the United States, where the electoral college has delivered a president who has thrown everything into doubt yet has no desire to alter the con­stitutional architecture that delivered him victory. A partisan, archaic, gerrymandered, dysfunctional system helped to engender the frustration that gave Trump his chance. Now President-Elect Trump plans to govern by deploying the full resources of that broken system. He represents a doubling down on the dysfunction.

The situation in the UK is similar. The upheaval caused by the vote for Brexit has had the effect of entrenching many of the features of our constitution that were most in need of reform.

The House of Lords, still basically unreformed after decades of politicians’ promises to sort it out, now finds itself being held up by opponents of a hard Brexit as a means of resistance to complete EU withdrawal. The first-past-the-post system has produced a government that is both relatively weak and enormously powerful: deciding what Brexit means lies with a small group of ministers whose party barely has a majority in the Commons.

If the Tory government seems overwhelmed by the challenge of Brexit, that is in large part because our political system puts too much power in too few hands. Yet the effect of this pressure to deliver is for the government to circle the wagons and draw the strings of decision-making closer together. Theresa May is doubling down on the centralisation of the British state.

The one big change that is coming is likely to reinforce rather than disrupt the status quo. The planned redrawing of constituency boundaries gives the Conservatives no reason to change the electoral system. Meanwhile, it gives Labour the excuse it needs to use reselection as a proxy for fighting its internal battles.

The result will be to drive the two main parties further apart. It will not improve the prospects for reform that finds common ground across partisan divides. The Brexit battles will be fought through a system that is likely to widen the divisions that made Brexit possible in the first place.

The British constitution is changing all the time; precisely because it is not codified it can be adjusted almost at will, and there have been several adjustments in recent years, particularly in relation to devolution. However, this usually happens more or less by stealth, without any of the fanfare that attends constitutional reform in other countries.

How many people in Britain were even aware that we had a Supreme Court, until they discovered that it was being asked to intervene in the process of how Article 50 might be triggered? Now those same judges find themselves at risk of being branded enemies of the people. One case for the British constitution has always been that it is inherently “political”, which means that it can evolve with the times. But when politics itself is as fractured as it is now, a “political” constitution risks getting fractured along with it.

The great irony of Brexit is that a revolt against the established order has so far done nothing to force the established order to rethink how it does its business. Brexit has sucked power back into the Whitehall and Westminster institutions with which many of those who voted to leave the European Union are so disgusted.

The gaping hole in the case for taking back control was always the absence of an argument for how political control would be ­redistributed within the UK. To put it in Ukip terms: what we’ve got is a Farage Brexit rather than a Carswell Brexit.

Douglas Carswell, still Ukip’s only MP, has long been one of the most vocal and provocative champions of a radical reform of the democratic system that would reflect the changing expectations and life experiences of the electorate. But his voice, and the voices of those like him, have been almost entirely drowned out by the cacophony of arguments about what Brexit means for basic challenges such as money, jobs and immigration.

These things matter far more to almost everyone than constitutional reform. But that is precisely why subsuming constitutional reform in the ordinary business of politics is so dangerous.

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There is a great risk that we have been thinking about Brexit back to front. We treat the political system as a vehicle for expressing what people are angry about. But what if their anger is a reflection of the failures of the political system? In that case, by allowing politics to carry on as normal while trying to deal with the unprecedented administrative challenges of exiting the EU, we are in fact enabling the problems to fester. But where there’s a risk there is also a huge opportunity.

In the end, a politician such as Carswell isn’t going to make much difference – he is at the flaky end of his flaky party, which is going nowhere for now. For politicians of the left, however, there is a wide open space for radical thinking about how power is distributed in 21st-century societies, and how our democratic system must find ways to distribute it more effectively.

Some of that, as I wrote in the last New Times special (NS, 23 September), demands hard thinking about the digital revolution and its consequences. But some of it is simply the bread-and-butter business of constitutional reform. Change the voting system! Democratise the second chamber! Empower local government! Deepen devolution! Just because there are many other things going on that seem more pressing doesn’t mean now is not the time. Now is the time – otherwise, instead of opening up British politics, Brexit will just lock it up for another generation.

David Runciman is a professor of politics and the head of the department of politics and international studies at the University of Cambridge