‘Please do not waste this time,” Donald Tusk implored as he announced that the EU would be granting the UK another extension, this time six months, in order to avoid a no-deal Brexit. He shouldn’t have had to say it: it’s obvious that the next six months will be critical in finding a resolution to the political crisis that has engulfed Britain. But there’s every chance that the European council president’s words will go unheeded.

Six months is ample time for our politicians to grasp the nettle. But parliament remains gridlocked, with no majority in favour of anything, and it is difficult to see what more time can do, by itself, to fix this. The EU has been clear that while it is open to redrafting the non-binding political declaration, it will not reopen negotiations on the withdrawal agreement on the terms of our exit. So a majority of MPs backing the existing withdrawal agreement remains the only way for Britain to leave with a deal. That looks implausible. The DUP is unlikely to shift its position on the backstop and the hard Eurosceptic flank of the Conservative party has little incentive to fall in line when it can hold out for the new no-deal cliff edge at the end of October. And even as cross-party talks continue, a Conservative-Labour compromise on a softer form of Brexit is a remote possibility because it would probably split both parties irrevocably. For Labour, there is no way of ensuring that any guarantees Theresa May offers with regard to the future relationship would be binding – she or her successor could look to build a different coalition of support in parliament altogether to shape the relationship after the withdrawal agreement is passed.

The gridlock is a feature of a two-party, majoritarian political system that is only capable of resolving questions that divide along party lines, not those that cross it. It’s why a general election is unlikely to provide much clarity, even if it were to deliver a majority rather than a hung parliament. Neither of the two main parties looks capable of rallying around an unambiguous Brexit position, with clear water separating them.

Labour MPs should vote for May’s withdrawal agreement on the proviso it gets put to voters.

The only way out of this ruinous stalemate remains a confirmatory referendum on the withdrawal agreement. The principled case for this, which the Observer first made more than two years ago, remains as strong as ever. There was no firm Leave proposition on the table in 2016. Voters were told by the Leave campaigns that Brexit would result in Britain seizing back control, all the while freeing up vast sums of cash for spending on public services and boosting businesses. All that the result provided was a mandate for the government to negotiate the best exit terms it could get.

Now there is a firm deal, it would be unthinkable for parliament to ratify it without putting it back to voters, particularly given the gulf between what they were promised and what has been achieved. The reality of Brexit, with all its tough trade-offs – and the fact that there is no way of achieving a clean break from the EU that respects the Good Friday agreement – is embodied in May’s withdrawal agreement. The idea that voters should not get a say on the terms and conditions of the most important postwar decision facing Britain is preposterous. If the merits of that principled argument are not, in themselves, enough to convince, the pragmatic case becomes stronger with each passing week: there is clearly no other resolution to this gridlock in sight. Before the European elections, Labour will have to decide whether it is in favour of a soft Brexit compromise or confirmatory referendum. Labour MPs should vote for May’s withdrawal agreement on the proviso it gets put to voters. Not only is it the right thing to do, it will benefit Labour electorally: in almost every Labour seat, most Labour supporters voted to stay in 2016. As Richard Corbett, the Labour party leader in the European parliament, warns, a failure to do so would risk Labour leaching votes to other parties in the European elections.

A confirmatory referendum is not without risks. Another national debate could prove divisive. But there is no such thing as a good way out of this crisis; every path risks further division. Far-right populists such as Nigel Farage will seek to make capital out of every outcome; nothing will measure up to the fantasy he continues to promise voters. Rather than hoping the populist arguments will slink away as a result of some sort of soft Brexit compromise, we must take them on – and win.

If voters were to ratify the withdrawal agreement in a referendum, that still leaves a huge question about what form our relationship with the EU should take. This is too important to leave to the dominant faction of any one political party. In that scenario, parliament must consider setting up a national citizens’ assembly, selected to be representative of the country in terms of demographics and the Leave-Remain divide. We have reached a point where it is more likely that ordinary citizens can grapple with the gritty realities of Brexit and forge a pragmatic compromise than our elected politicians.

MPs should mark Tusk’s words. If they don’t back a confirmatory referendum, there is a real danger that we will be in exactly the same position come mid-October: both parties locked in internal struggles, no parliamentary majority in favour of anything, the prime minister on the cusp of requesting another extension with no plan for how to use it. Parliament can prevent this horror show from repeating itself. It must act now, before it’s too late.