A series of opinion polls published in recent days have shown something unprecedented in British politics: four parties locked in a statistical tie. The UK vote is now split evenly between the long-dominant incumbents — Labour and the Conservatives — and two challengers harnessing a Brexit backlash — the Liberal Democrats and the Brexit Party.

This four-way dead heat is more than a statistical curiosity: it could be the harbinger of a realignment. The powerful incumbency benefits of our first-past-the-post electoral system, which have long protected Labour and the Conservatives, depend on the established parties maintaining a lead over the upstarts. If that advantage is lost, first-past-the-post can be turned against the establishment with brutal speed.

The key mechanism here is not electoral, but psychological. If voters believe new challengers have no hope, they hold their noses and back the least-worst of the two incumbents. This protects the traditional parties and suppresses support for newcomers. But if voters start to believe the upstarts can win, locally and nationally, they no longer have to accept second best.

Think of it as the electoral “Tinkerbell effect” — if people believe new parties can win, then that belief becomes self-fulfilling. If people cease to believe the old parties are unbeatable, they become beatable.

This is the reason for the Liberal Democrats’ long-standing and much-ridiculed obsession with (often misleading) bar charts showing they are the only local opposition capable of “winning here”. The party knows, from long, bitter experience, that the biggest hurdle the electoral system throws up is in voters’ heads — convincing people they are a credible challenger is more than half the battle.

If the trickle of polls showing the Brexit Party or the Liberal Democrats ahead of both Labour and the Conservatives turns into a flood, belief in the old red and blue Tinkerbells may ebb away, and belief in the new yellow and turquoise Tinkerbells may take wing. The political landscape could then change overnight in a way we haven’t seen since Labour first emerged after the 1918 introduction of the mass franchise.

Of course, the recent polls may prove to be a European election-driven blip, with normal service restored soon after. But there are a number of reasons to think they may not be or, at least, not for long. Voters’ tribal attachments to the traditional parties have been eroding for decades, and the newcomers are mobilising deep divides in the electorate — over education, identity, diversity — that have been building for a long time.

Layered on top of that is the powerful divide over Brexit, which mobilises these structural divisions and cements them into new “Leave” and “Remain” partisan identities, more powerful than the fading attachments to the establishment parties. It is unlikely any Brexit outcome will bridge these divides or satisfy the increasingly polarised voters of the two Brexit tribes.

The established parties might stand a chance if they had charismatic and popular leaders who could combat the appeal of purist alternatives on Brexit. Yet this is not the hand fate has dealt them. Jeremy Corbyn is, by any measure, one of the most persistently unpopular and divisive leaders the Labour Party has ever had, and his attempts at compromise on Brexit have resulted in a stance which few voters understand and most voters dislike.

Theresa May is leaving office with miserable poll ratings, having united the country in opposition to her Brexit proposals. None of the football squad of Tory hopefuls vying to replace her looks much more popular. Whoever succeeds in the contest will face the same impossible Brexit dilemmas that have undone her premiership. Their early campaign exchanges do not suggest much willingness to even think about these, let alone overcome them.

Rapid realignments of party systems have happened before under first-past-the-post. Canada has had two in the last three decades — in 1993 when the governing Progressive Conservatives collapsed, losing 154 of their 156 seats, and in 2011 when the New Democrats supplanted the Liberal Party. The Liberals bounced back, the Progressive Conservatives did not.

We have also seen the process unfold closer to home, and recently. In Scotland, just four years ago, the Labour Party, which had dominated Scottish politics for generations, lost 40 of its 41 seats, following the largest swings seen in any constituent UK nation since the 1918 Irish election, when Sinn Fein swept aside the Irish Parliamentary Party in the last contest before the Irish Republic's departure from the Union.

The Westminster political conversation moved on too quickly to Brexit for the lessons of that result to be absorbed. Scottish Labour’s annihilation shows no party, no matter how deeply rooted in class, regional, social and national identity it is — has a right to rule, or even to exist. Then, as now, the forces of electoral destruction were unleashed by a closely-fought constitutional referendum.

It would be hard at the best of times for the parties to retain the loyalties of an electorate which respects neither their leaders nor their policies on the dominant issue of the day. With no end in sight to the Brexit crisis, it may prove impossible.

It is a remarkable coincidence that, at the very moment that two new parties are making a credible bid to break Britain’s long political duopoly, a by-election is being held. If one or both of the new challengers can overhaul the big two in Peterborough on Thursday, it may begin a feedback loop, with success reinforcing credibility, which in turn begets further success.

Perhaps historians will one day see this by-election as the first act of the great Brexit realignment. It looks unlikely now, but then, as rueful Scottish Labour or Progressive Conservative politicians will testify, these things always do until suddenly, they don’t.