In their Brexit stand-off, both May and Corbyn are in fear of their own MPs

Both party leaders have aptly demonstrated in the past that there is no button either can press to make their MPs do their bidding. 

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Theresa May has survived a vote of confidence in her government and has opened talks with the opposition parties to resolve the Brexit stand-off. The parliamentary leaders of the SNP, Liberal Democrats, Plaid Cymru and Caroline Lucas, the sole Green MP, have all either taken part or are doing so now.

Those talks have so far yielded little because all five of those parties want something – a second referendum – that May doesn’t want to give.

But Jeremy Corbyn has refused to participate unless or until the Prime Minister rules out the possibility of a no-deal exit, which his aides have described as tantamount to blackmail. (May’s behaviour, that is, not Corbyn’s.)

It’s true to say that only parliament can rule out a no-deal exit, by striking the legally mandated exit date out of British law and then passing a motion calling for either Article 50 to be revoked or an extension to be sought. (Although extension is in the gift of the 27 other member states and revocation can only occur to end Brexit, not to buy the departing nation more time, the view among EU diplomats I have spoken to is clear: in the event that an extension is needed to prevent no deal, one will be forthcoming just as it would be for another referendum or an election) So May cannot rule out no deal alone but she could offer to bring forward legislation that takes no deal off the table.

She doesn’t want to do so because it would cause political ructions in the Conservative party, and also because the looming threat of no deal is her single best asset, not least while Conservative cabinet ministers are still ruling out any policy concessions, whether on the single market or the customs union, that might make the withdrawal agreement more palatable.

So who’ll blink first? A lot depends on two factors outside either’s control. The first of course is who voters think is behaving irresponsibly. Today’s print headlines aren’t as bad for the Labour leader as you might expect but, were I Labour, it would alarm me that the version of the story as condensed to fit a one-minute bulletin between symphonies on Radio 3 this morning (and the near-identical version that will have played on Radios 1, 2, 5 and 6) highlights that everyone else is taking part in talks while Jeremy Corbyn is refusing to do so.

The second is backbench MPs. As both party leaders have aptly demonstrated in the past, there is no button in Downing Street or in Norman Shaw South that they can press to make MPs do their bidding.

When you talk to Labour MPs, most will say at first that they have no intention of caving into May’s blackmail and that they will fight to the last barricade for a Norway-Plus Brexit or a second referendum or what have you. But I think the glum minority who will concede that when it comes down to it, neither they nor their colleagues will permit a no-deal Brexit even if they have to vote for May’s deal to do it, have a better gauge on what will actually happen if the crisis runs on.

But May can’t control her backbenchers either and Labour MPs’ salvation might come in the shape of a backbench effort from Tory MPs Nick Boles, Nicky Morgan and Oliver Letwin, which, if passed, would mean that in the absence of agreed solutions to the Brexit crisis within the next few weeks, May will be bound to seek an extension of the Article 50 process.

So the real question isn’t which one of May or Corbyn will back down, but who should be more worried about the MPs behind them.

Stephen Bush is political editor of the New Statesman. His daily briefing, Morning Call, provides a quick and essential guide to domestic and global politics.