Parliament’s verdict on Theresa May’s Brexit deal is struggling to match its billing as a “meaningful vote”, since no one can say what the prime minister’s defeat would really mean. It is especially unpredictable because the battles to come will not run along party lines. Many MPs decided long ago that their Brexit choices transcended attachment to a red or blue rosette. They might have party whips on their backs, but they feel history’s eye on them more keenly.

One Labour veteran, witness to many a parliamentary rebellion, describes loyalties in the Commons today as the most fluid since the repeal of the corn laws 172 years ago. That tussle over tariffs brought down a prime minister, split the Conservative party and created a new Liberal one.

Today’s Tories look more divided than Labour, but that is because a governing party has to do Brexit, while the opposition only has to talk about it. May has made unpopular choices that Jeremy Corbyn pretends do not need making. Labour’s policy is to engineer a general election, win it, then cook up an alchemist Brexit that keeps the benefits of the single market without the obligations of EU membership. The unavailability of that combination has been proven many times.

If Tory MPs cared only about party unity, they would rally behind May’s deal. Their goal would be to get over the finish line without sweating over the small print, mint the commemorative coins and change the subject – enjoying the respite of a transition period before too many people realised they had been diddled. But neither hardcore leavers nor remainers are prepared to play along. Tory Brexit ultras demand a new deal, knowing there is no time to get one. They are just flapping their arms in anticipation of a run at the no-deal cliff edge. But if that is the way things are heading, many pro-European Tories would take their chances on a referendum with a view to aborting Brexit altogether.

For the hard-right Conservatives, Brexit is one stage in a still more radical project – a hybrid of Ukippish nationalism and deregulated market free-for-all. Tory moderates dream of rehabilitating their party’s one-nation tradition and its social conscience. May is still in office mainly because a leadership contest would prise that ideological schism open beyond repair. No Tory can name a candidate to unite the party; many can think of someone whose victory would force them to quit.

Corbyn has more job security than May, but it is built on a devoted membership, not a loyal parliamentary cohort. Even if Labour MPs vote en bloc against the Brexit deal it will be for divergent reasons. Some share the leader’s ambition to provoke a dissolution of parliament. Others dread a general election, but think it unlikely and expect party policy to switch to a second referendum as the next best thing. A third tranche is torn between the impulse to satisfy leave-voting constituents and hatred of May’s government. They want Brexit done, but will avoid throwing the prime minister a lifeline when the waters are closing over her head.

Corbyn himself does not seem naturally interested in Britain’s EU membership. His most commonly stated preference since the referendum has been to leave on terms that remove the UK from single market rules on competition and industrial subsidy (a pretty hard Brexit). But he is mindful that many of his supporters wish he would rally for remain. Corbyn’s ideal outcome would probably be to get Brexit with none of the blame for Brexit. So the Labour leadership has circled over May’s government like vultures, watching a wounded creature crawl across an arid plain. There are worse strategies. Scavenging is an effective evolutionary model, albeit not an inspiring one.

Corbyn has reasons to avoid getting involved in the People’s Vote campaign. It would put him in public alliance with liberal Tories and Blairites, the kind of people with whom he does not share platforms (including the actual Tony Blair). The opposition leader’s team also suspects the People’s Vote movement of incubating a new party and sees no value in political insurgencies outside Labour’s control.

That isn’t entirely paranoid. There are Labour MPs who want a referendum but would not be too disappointed if their leader were to be seen to obstruct one. That decision would give moderate rebels a cause to break with the party on terms that might carry some sympathy with the membership. For Corbyn to be exposed as unequivocally pro-Brexit would test the faith of all but his most dedicated acolytes. The remnants of pre-2015 Labour would fall away and the party, for better or worse, would emerge purely Corbynite.

What form that rupture takes is unclear. Volatility shakes up old allegiances but it doesn’t remove all obstacles to the establishment of new parties. The electoral system still punishes political startup ventures. A craving for different leadership doesn’t conjure ideal leaders into being. And the call of the tribe should never be underestimated. In an election, many MPs who claim now to have floating loyalties would drift back to their original side.

Many, but not all. Much depends on how long the turbulence lasts and how extreme it gets. England’s two main parties are sailing into a rare constitutional hurricane and it isn’t clear whether their vessels are sound. All manner of things will be thrown overboard – policies, MPs, leaders. Some will jump before they are pushed. The parties that emerge on the other side of this storm will not be the same ones we have now, even if they sail under familiar names and colours.

• Rafael Behr is a Guardian columnist