What are the obstacles to a softer exit from the European Union – or no exit at all? They are, in descending order of importance: public opinion, Labour MPs in the West Midlands and Yorkshire, Eurosceptic Conservative MPs, the question of whether or not Article 50 is reversible, and Jeremy Corbyn’s Euroscepticism.

The latter has had more column inches devoted to it than anything else: it’s true that the Labour leader’s private belief is that Britain is better off out. He was persuaded to take a role in the Remain campaign, albeit one that frequently frustrated the official campaign, partly to retain the leadership, and partly because Yanis Varoufakis convinced him that Brexit would lead to the break-up of the European Union and an even worse deal for the nations of the EU’s southern perimeter.

That the EU doesn’t look remotely likely to break-up as a result of Brexit means that Corbyn’s old Euroscepticism is back in vogue, but the Labour leader doesn’t, as one ally puts it, “have religion” on the issue. (As I explain in my column this week, Corbyn’s passion project is foreign policy, and like most Labour politicians, he doesn’t really regard the EU as properly abroad.)

Although there are committed Eurosceptics with a powerful voice in the leader’s office, there are also a number of Europhiles. Corbyn’s position is essentially to have a quiet life internally and to find ways to defeat the Conservatives wherever possible, both of which push him towards a more Europhile position.

But the reality is that the Labour leader’s position is not all that important as far as Britain’s Brexit trajectory goes. The party’s position is, but that is set through the competing interests of the membership and trade unions – who largely favour retaining Britain’s single market membership – and the parliamentary Labour party – where a narrow majority favours a more drastic Brexit. That’s why the preferences of Labour MPs in the West Midlands and Yorkshire, the group most likely to be committed to a version of exit that ends the free movement of people, bringing with it a big breach from the European Union, are a lot more important than Corbyn’s feelings about the rules of single market membership.

An equally important block to a softer exit are committed Eurosceptics on the Conservative side. Taken together, the votes of Conservatives who are ideologically committed to a drastic Brexit or believe that only a drastic breach from the European Union can uphold the demands of Leave voters, plus those of Labour MPs who are ideologically committed to Brexit (not a very large group but every vote counts) and those Labour MPs who believe that a drastic Brexit is the only way forward (a significantly larger bloc) means that it is difficult to get 325 votes for an alternate strategy.

Then there’s the problem that while few voters, whether they backed Remain or Leave, have changed their minds, there is a large majority that believes the referendum must be upheld – and that majority also believes that “upholding the referendum” means a drastic breach from the EU.

It’s not clear what coagulating the narrow minority of MPs who currently back a softer version of exit into a new party (parking for a moment where the SNP, Greens and Plaid Cymru fit into this) does to peel off recalcitrant members of Labour or the Conservatives who might one day back a softer exit but are currently voting and arguing for a more drastic breach.

It might give a bigger platform for someone arguing for a gentler exit, perhaps helping to turn public opinion. But given that at present so few MPs are interested, talk of a new anti-Brexit party feels like displacement activity, rather than a serious attempt to stop Brexit.