British Prime Minister Theresa May walks after holding a press conference on the first day of an EU summit focused on Brexit in Brussels on Friday. Agence France-Presse

The BBC’s political editor, Laura Kuenssberg, went so far as to end her report on Wednesday night’s BBC News at Ten by asking: “What is working now? Not the machine around the prime minister, nor our political parties, nor our parliament.”

Earlier that evening in a rare broadcast to the nation, the prime minister had managed, if that were possible, to make things worse, when she spoke of her “deep personal regret” that Brexit was having to be delayed, blaming MPs, with their “political games and arcane procedural rows” for the mess.

Next morning, before the European Council meeting, Ireland’s prime minister publicly described the political situation in London as “chaos”. Oh, woe is us, indeed.

In a way, however, it could be argued that the breakdown of the political system – which is surely what we have been witnessing in recent weeks – is not just the inevitable consequence of a misguided referendum, but evidence of a profoundly dysfunctional system and a compelling argument for change.

First, the breakdown. It may well be a positive development that parliament has come into its own and that the UK public appears unusually engaged in day-to-day politics – watching Parliament TV, and even upping the viewing figures for the ailing BBC Newsnight. Nor are those “arcane procedural rows” Theresa May condemned in her broadcast to be dismissed so glibly.

They are the only way a fractured parliament has found to try to deal with the acute disunity in the Commons.

The extent of the institutional breakdown over the past two weeks has elicited expressions of surprise and shock, and there have been scenes in parliament without precedent. MPs from both main parties have regularly crossed the floor; whips, when imposed, have been defied. Discipline has frayed even inside the government.

On one crucial vote, several cabinet ministers abstained. At one point, a cabinet minister gave a speech making one argument, only to go into the lobby for the opposite. These are not “normal” times.

But should there really be shock? The divisions on “delivering” Brexit in the House of Commons are no more than the logical consequence of decisions made by David Cameron after his unexpected victory in the 2015 election. That seems like an aeon ago now.

But his decision not only to honour his campaign promise to hold an “in/out referendum” on EU membership, but to legislate for a referendum that lacked all the safeguards most countries more used to holding referendums routinely include – minimum turnout and a two-thirds majority, or other substantial margin – has contributed mightily to the mess. Should a Leave vote by 37 per cent of the electorate constitute a mandate for a hard Brexit, a soft Brexit, or no Brexit at all? That remains in dispute, not least because, left to themselves, a big majority of MPs would vote to remain.

Cameron’s other decision – which, unlike the terms of the referendum, was unavoidable, because a large part of the purpose was to settle the internal dispute in the Conservative Party – was to suspend parliamentary and cabinet discipline for the duration of the campaign.

Thus it was that prominent ministers and MPs from both major parties were out campaigning on both sides: Europe was treated as an exception for the purposes of party discipline – and it will remain so until the issue is resolved.

David Cameron might have managed the internal party divisions more adroitly than Theresa May has, but it is not something that he or any other prime minister would have been able to resolve.

This is because Europe is an issue – not the only one, but by far the most salient – on which the UK’s two main political parties are, and have long been, divided within themselves. Party allegiance and views on the EU do not match.

By rights, Theresa May’s snap 2017 election should have been fought on the EU issue, but the party political system we have could not reflect that. The result was not just a catastrophe for May, but greatly contributed to her troubles today.

But it is not just that the two main parties are divided on Europe and that the House of Commons has an anti-Brexit majority that conflicts with the referendum result.

It is that the way UK politics has traditionally been conducted – through adversarial debate, and winner takes all – is not conducive to the give-and-take that will be needed if the prime minister’s Brexit “deal” – or something like it – is to pass.

Contrast such basics as the layout and procedures of the UK parliament with those of almost any other modern legislature – including Scotland’s.

While our government and opposition sit opposite; their chambers are invariably hemispheres; while our parliamentary debates are rhetorical duels, with cheerleaders on either side, theirs are conducted more as genteel arguments, even conversations.  

In most of the continental European systems, what is more, compromise and concession are built into the system, fostered by an electoral system that gives due representation to smaller parties and allows better reflection of change.

In a more representative system, the UK would have two leftish parties, for and against EU membership, and two rightish parties (ditto), the Liberal Democrats and the Greens would have more MPs than they do today, and there might be room for Ukip, too (unless it merged with the Tory Eurosceptic right).

There was a time, between 2010 and 2015, when the UK had a glimpse of another way. Dismissed as likely to collapse in its first month, the Conservative-Lib Dem coalition survived more securely to full term than many a government before it.

It also – or so it seemed – made fewer mistakes of the Chris Grayling kind, perhaps because other views could be heard in cabinet before decisions were made.

It is said that David Cameron included his EU referendum pledge in his 2015 manifesto only because he expected to form a new coalition, and abandoning it could be a cheap concession to the Lib Dems. Alas, it was not to be.

It is hard now to imagine a time when the Brexit shambles will be over. If and when it is, however, this humiliating experience surely demands that we take a new look at how the UK is governed.

The aim has to be for the executive machine, the political parties and parliament all to reflect this multifarious country far better than they currently do, while eliminating the obstructiveness and rancour so evident today.