Jeremy Corbyn has ended the cross-party Brexit talks with Theresa May, citing the instability within the ruling Conservative party as the reason why he no longer believes that an accord can be reached between his party and May’s in an open letter to the Prime Minister.

What’s striking about this letter is what’s not in it: there’s no attempt to blame May, or the ministers participating in negotiations, for the failure of the talks. Indeed, the Labour leader goes so far as to praise the “good faith” in which government ministers acted, and the “detailed” and “constructive” tenor of the talks.

Instead, Corbyn has opted to blame divisions with the Conservative party, which have seen guarantees made in the talks called into doubt, whether due to backbench opposition to a customs union with the European Union – the Labour leadership’s central negotiating ask – or to the commitment of Liam Fox, the International Trade Secretary, to allowing American chemical-washed chicken into British marketplaces.

In a way, that is just canny politics: Corbyn doesn’t need to defeat Theresa May at the next election, because she will not be in frontline politics anymore. He is highly unlikely to have to defeat David Lidington, the well-liked Cabinet minister leading most of the talks from the government’s end, either. It doesn’t really cost him anything to indirectly praise Lidington’s approach to the talks.

But it also reflects one essential truth of the Brexit deadlock, which is that, in practice, what Corbyn is saying is that Labour will continue to vote against the withdrawal agreement until the Conservative party can speak with a single voice on the European issue. That is to say, a Labour opposition will never vote for a withdrawal agreement put forward by a Tory Prime Minister.

It represents at the least a setback and potentially a permanent defeat for the Labour leadership’s preferred tactic at the next election: which is to be able to go to the country with Brexit resolved, running on a ticket of broad discontent with the condition of the public realm, rather than having to pick a side of the Brexit duality.

That is, at least in part, due to the political success of the various pro-Remain parties: in Scotland and Wales, the SNP and Plaid Cymru, and in England, the Liberal Democrats, and the failure of participation in the talks to quell the rise of the Brexit party.

But Corbyn retains the option of backing a Brexit resolution that can command a majority via votes on the floor of the House in his letter, saying Labour will “carefully consider” any votes brought to the Commons.

The reality, of course, is that without an election, it is highly doubtful that any such resolution exists. The most important consequence of this letter is that it further suggests there can be no resolution to the Brexit deadlock with this parliament.