Plus ça change, as President Macron might have said, but probably didn’t last night at the Brussels summit. Another Brexit extension has been granted, this time until the end of October. A breathing space in which to decide when – and indeed whether – to leave the European Union. Something, surely, has to give to allow that choice finally to be made?

The first thing to note is that the new deadline is shorter than the nine-month delay suggested by European council president Donald Tusk, and that this has consequences. It puts enormous pressure on those who support another referendum. Analysis by colleagues at University College London puts the time between parliament deciding to hold one and the vote itself at around 24 weeks. MPs, therefore, would have to agree to hold such a vote within the next few weeks in order for there to be sufficient time to stage it. It remains hard to see how a majority for such an outcome could be marshalled in time.

The summit has also increased the pressure on the prime minister. For all Theresa May’s insistence that she intends to hang around to get the job done, this choice may not rest with her. Indeed, were she even to survive that long, it’s hard to see how local or European elections will serve to convince Tories they’re being led by a winner.

One way or another, therefore, I suspect the Tories will enter leadership contest territory. Whoever is elected, however, will be confronted by the same parliament – the same lack of majority for anything, the same divisions on his or her own benches. The current parliamentary numbers don’t imply a happy sojourn for the new incumbent of No 10 – which raises the possibility of a general election. And despite the abject performance of this government, the Tories are more or less holding their own in most of the polls. A new leader, enjoying a brief honeymoon period, and having perhaps convinced the chancellor to loosen the purse strings, might fancy his or her chances.

And, contrary to what many say, a general election would change things. Both parties, for one thing, would be forced to produce manifestos specifying their intentions. And the campaign would provide an opportunity to ensure that all candidates sign up for these manifestos. Where’s the fun, after all, in leading a party if its MPs simply vote however they wish?

And so, following an election, what then? We know all too well what is not possible. As yesterday’s European council made clear yet again, there can be no reopening of the withdrawal agreement. So if we want to leave with a deal, we will – eventually – have to approve that much maligned document.

However, new parliamentary maths implies new political opportunities. Imagine, for instance, that the Tories manage to form a government without relying on the Democratic Unionist party. Most conceivable successors to May would seek a more distant relationship with the EU than that specified in the withdrawal agreement. And they could achieve this by signing up to a Northern Ireland-only backstop. Equally, should Labour triumph at the polls, it may have the numbers to negotiate and ratify a softer Brexit outcome.

However uncertain the outcome, an election could represent a way out of the current impasse. If parliament won’t shift, then the parliamentary numbers must be shifted.

So what now? There will be another EU summit at the end of June, which will carry out the “stock taking” exercise insisted on by the French president. And if the UK fails to hold European elections on 23 May, then Brexit will happen on 1 June. The prime minister, for her part, can still cling to the hope of getting parliament to agree to her withdrawal agreement. If she gets her skates on, it’s still just about conceivable that she can get it done before the European elections, though don’t bet on that.

All things being equal, however, the clever money must now be on the 31 October deadline. It’s not as if the sound of a ticking clock has inspired parliament to decisive action to date. May failed to convince wavering MPs to back her deal even with the real prospect of no deal looming, so it’s hard to see how she can do so now. If she stays, it is hard to see how this ends.

• Anand Menon is director of The UK in a Changing Europe and professor of European politics and foreign affairs at King’s College London