An attempt to find a Tory-Labour compromise on Brexit was the right response to Brussels postponing the March date for the UK’s departure from the EU. Today it seems likely to fail. There is clearly no algorithm whereby Theresa May and Jeremy Corbyn can agree on a mix of customs union and confirmatory referendum that might win a Commons majority. That being so, it is likely that there will be a different attempt to mobilise such a majority on the benches of the Commons, outside the bounds of party loyalty. MPs will be asked to indicate what sort of Brexit they would like, stumbling for a way forward through the wreckage of their leaders’ failure.

They must not be distracted by the forthcoming European parliament elections. The looming apotheosis of Nigel Farage’s Brexit party may once again show the daftness of simplistic populism. However, as last week’s BBC documentary Brexit Behind Closed Doors showed, Farage can bellow as much as he likes but it will not resolve the contradiction of “frictionless Brexit outside a customs union”.

Frictionless Brexit remains a contradiction in terms. A rerun of the 2016 referendum is not going to happen, even as public opinion polls seem to swing marginally towards remain. The best hope of a second vote is to confirm any new deal once one has been agreed by parliament and Brussels. MPs must decide what that deal should be. It would seem, from the last round of indicative votes, that a custom union/single market option would garner most support. It would reflect the broad centre of opinion in parliament – including the minority parties – if not for remain, certainly against a disruptive Brexit.

When we were here before, with the March indicative votes, MPs funked a decision. What might have been a vote for Brexit within a European economic space, however defined, dribbled away in party factionalism. The extremes were left to defeat the centre. This cannot happen again. MPs are again on parade and must be positive. The obvious way of achieving this is by transferable votes between options.

A greater challenge then presents itself. The Commons must empower a plausible executive machine to deliver what it decides. The party leaders must agree in advance to implement that decision. This would require the Tories to support May, still their leader, to present Brussels with whatever the Commons has decided, irrespective of what the Tories alone decided. To carry any credibility, the prime minister would need other Commons parties alongside her.

The Commons cannot merely indicate how it wants the government to proceed with Brexit, if it then denies a majority in parliament for implementation. If it did that, we would be back to our old friend, square one. Since the only decision parliament has so far emphatically taken is against no deal, the only remaining option would be for a deputation of MPs to beg Brussels for another extension – an exceedingly long one.

• Simon Jenkins is a Guardian columnist