Across Europe, old two-party political systems have been fragmenting for a generation and more. In most western European countries, the left-right split has long been overlaid by others, notably on social values and identity. Germany now has seven significant parties in the Bundestag. France has at least nine in a national assembly dominated by a party that did not even exist in 2016. Ireland’s Dáil has 10 and more. Spain’s outgoing congress of deputies some 13. Part of this fragmentation can be explained by differences in electoral systems and in national histories that make multiparty outcomes more likely. But not all of it. The fragmentation also reflects the fact that all societies have evolved in the post-industrial era, and that politics has had to adjust.

Is the same thing happening here? It already has done in Scotland. The abandonment of the Labour and Conservative parties by 12 MPs this week suggests it may be happening in England, too. Britain’s old duopoly was challenged in the 1970s and 1980s. The process did not go as far or fast as it did elsewhere, partly due to our first-past-the-post system. But the same stresses and strains were there, helping to boost parties like the Liberal Democrats, Ukip and the nationalists. The 2017 election saw a swing back to the old parties. Now, fragmentation may be resuming. It would be ironic if, as Britain leaves the EU, British politics become more firmly European.

At the very least, the emergence of the independents introduces a new element of parliamentary and political uncertainty into the already tense calculations around Brexit. It is possible, for instance, that the switches from Labour may increase the pressure on Jeremy Corbyn to bend towards the defectors’ agenda of a second referendum, in the hope of staunching other departures. Equally, the defection of three Conservatives may ratchet up pressure on Theresa May to stem further exits to the independents by agreeing to rule out a no-deal Brexit. Neither change of stance would be in character for either leader, but events may force their respective hands in the coming days.

There is an obvious danger that more will be read into the past week’s shifts at Westminster than the events deserve. Twelve MPs is not a big number. More than 300 MPs have switched allegiance at various times in the past 120 years, yet though Labour replaced the Liberals in the 1920s, a duopoly has endured. This week’s switchers are not household names in the way that Roy Jenkins and Shirley Williams were when they formed the SDP in 1981; the independents currently lack the activists, money and cause that brought that earlier insurgency close to real power.

But this week should not be underestimated either. Both the Conservatives and Labour are at risk of lasting and simultaneous fracture. Brexit is breaking the Tory party in front of our eyes. If the fanatics replace Mrs May with one of their own this summer, a much deeper breach is inevitable. Meanwhile, Jeremy Corbyn’s Glastonbury phase feels over. The question to be asked about the revolt against him on Europe, antisemitism and wider internal bitterness is about the scale of the damage, not whether it is taking place.

Brexit has taken party politics to a very troubled place, which was highlighted by the unmistakable and very human sense of liberation and relief displayed by the switchers this week. The 12 do not control the political agenda. But they pose a challenge to every party, big and small. To respond with abuse or the old tribalism is not just wrong in principle. It is to miss the point. The point is that the old politics has failed, and that a modern Britain should want better.