Over the next few weeks, Britain faces a stark binary choice. It is not the blackmail choice that Theresa May misleadingly poses: my deal or no deal. Nor is it the choice Jeremy Corbyn still implausibly claims: her bad Brexit or his much better Brexit. The real choice we must make before B-day (currently 29 March) is this: blindfold Brexit or democratic timeout.

As parliament takes back control, we urgently need the Labour front bench to join MPs from all parties in getting us to the timeout. By timeout I mean a period of democratic deliberation leading up to a second referendum, in which we decide, on the basis of everything we now know, how we should address the real problems that contributed to the vote for Brexit in 2016, what kind of country we really want to be – and whether we can do that better outside or inside the EU. For this, our EU partners will extend article 50 and give us the necessary time.

Everything else – May’s deal, no deal, customs union, Norway plus, Canada plus, common market 2.0, make your own label – is just a variant of blindfold Brexit. This clarifies what might otherwise appear like total confusion. In all these variants, what Brexit actually means would only be determined in a drawn-out negotiation after we had left the EU. And once you are out, you are out. Whatever the goals set by the British government – and both the government and the goals might change – we would be negotiating from a position even weaker than we are in today. As Ivan Rogers, our former permanent representative to the EU, has warned, those negotiations would be “tougher than anything we have seen to date”.

‘Jeremy Corbyn’s speech in Wakefield on Thursday remained in depressing denial-and-diversion mode.’ Photograph: Sean Smith/The Guardian

A Labour government coming to power in these circumstances would be like a street cleaner having to gather the horse dung after a Tory hunt has passed down the high street. It wouldn’t be long before the public started blaming Labour rather than the “Tory Brexit”. One of the delusional ideas still whirring around Westminster is that, having “done Brexit”, we can rapidly get back to addressing our real problems, such as housing, health and education. Brexit won’t be done for a decade, and the economic cost of even the softest Brexit will leave less money available for already stretched public services. The people hardest hit will be Labour’s working-class voters.

Another delusion is that it’s up to us to decide whether to extend article 50. Not so. It also requires the unanimity of the EU 27. Nobody knows what EU leaders would do in extremis, but they have repeatedly said that they will not extend it just for more negotiations. There could be a short technical extension to allow Britain to push through the necessary legislation. Otherwise, it would require a clear determination from London to have a referendum or a general election with the option of Britain remaining in the EU. As one seasoned observer puts it: you need an extension to have a referendum, but you also need a referendum to have an extension.

Here, then, is the choice before Labour. Corbyn’s speech on Thursday remained in depressing denial-and-diversion territory: elect a Labour government to negotiate a better Brexit, but the real problem is a suffering majority that has been immiserated by a rapacious elite. This is just cakeism with red icing. In the next two weeks, the choice will become real.

Unless something wholly unexpected happens, May’s deal will be voted down next Tuesday. Labour will then propose a motion of no confidence, potentially leading to a general election – but that motion, too, will be defeated. If the government respects the cross-party amendment dramatically voted through the House of Commons this week, it should come back within three parliamentary working days of Tuesday’s vote to say what it proposes to do next. Since the house is currently not scheduled to sit next Friday, that brings us to Monday 21 January.

May has got all the Irish backstop reassurances that she is likely to get out of Brussels. Unless a significant number of Labour MPs swallow the mind-stretching proposition that a post-Brexit Conservative government is going to be a better protector of workers’ rights than the EU, an attempt to push her deal through on a second vote will fail. If the dissident Conservative Dominic Grieve and his fellow signatories to that cross-party amendment are supported in their interpretation by the Speaker, there will be the possibility of amendments to the government motion. By this procedural means, or an explicitly “indicative” vote, parliament could test the support among MPs for different options.

‘A new people’s vote would be a referendum on Britain’s future.’ Photograph: Antonio Olmos/The Observer

Crunch time for Corbyn comes then, or very soon thereafter. If he can overcome his own Lexiter (leftwing Brexiter) instincts, then Labour can lead a cross-party parliamentary majority to take the Brexit question back to the people, in a well-prepared second referendum. The onus would then be on the government to respect the will of parliament and put through the necessary legislation. If it refused, or proved incapable, then parliament itself would have to take even more decisive control over the process. A benign side effect would be to curb what is still an over-mighty executive, and create a more modern, democratic balance between legislature and executive.

The very method of getting to a second referendum will already have demonstrated something of crucial importance: that this is not simply a repeat of the first. It’s not Blairite, metropolitan, liberal elites telling the benighted people to vote again until they give the right answer. No, this is part of a much larger process – perhaps including a citizens’ assembly, as suggested in a recent Guardian editorial – which is a positive democratic response to the vote for Brexit. If this verbless phrase does not sound too Blairite for Corbynist ears: tough on Brexit, tough on the causes of Brexit.

So this process would be as much about understanding the real causes of the Brexit vote, and addressing them, as about our relationship with the EU. The new people’s vote would then be a referendum on Britain’s future – who we think we are, what we want to be, and how we best get there. A convention being held in London today aims to kickstart this debate.

For Labour to understand the real binary choice that we face – blindfold Brexit or democratic timeout – and plump decisively for the latter would be the best thing for the whole country, and for Europe. It would also, incidentally, be welcomed by a large majority of Labour party members and supporters, while further dividing the Conservatives.

I don’t for a moment underestimate all the difficulties down this route. There is no good way out of the mess Britain has got itself into. But this is the least worst path, bringing unexpected possibilities for democratic and national renewal. Go for it, Labour – or the party, this country and our continent will regret the missed opportunity for ever more.

• Timothy Garton Ash is a historian, political writer and Guardian columnist