It’s all kicking off. A poll carried out by ICM for the Guardian showed that, excluding those with no opinion, voters support the idea of a second referendum by a 16-point margin.

Simultaneously, there are signs that the parliamentary battle over Brexit is about to become more joined up. The main groups opposed to Brexit have agreed to pull together under the banner of the grassroots coordinating group (GCG) in an attempt to ensure a popular vote on the outcome of the Brexit process.

Conservative remain supporters Anna Soubry and Ken Clarke have tabled amendments to the customs bill and the trade bill which would effectively keep the UK in the EU’s customs union. Meanwhile, senior figures in the Labour party are due to meet for talks that many think will herald a major policy shift towards backing for membership of a customs union with the EU.

Consequently, some commentators now argue that a second referendum is more likely than ever, possibly via an amendment to the bill implementing the withdrawal agreement that makes a fresh referendum compulsory. And remainers are beginning to hope that all is not lost.

How realistic are they being? Let’s assume, first, that the GCG manages to avoid the kind of People’s Front of Judea tribalism that has haunted the remain camp to date, that egos and ambition do not trump unity. Is it conceivable that parliamentarians would vote down or amend the deal the prime minister presents them with in October?

As my colleague Jonathan Portes argued some weeks ago, if MPs are genuinely interested in having a “meaningful” vote, they need to have it long before the government is offering it. A vote on vague aspirations in October is hardly satisfactory, if only because there will be no time left to negotiate a better deal with the EU.

Rather, parliament should be insisting now on a binding vote on the guidelines the government must draw up in the next month or so on its approach to trade talks.

The vote in October will, in practice, be a decision to reject the government’s whole approach to Brexit and start again

Practice in other states is instructive. In Germany, the Bundesrat provides “quasi-binding” advice to the government in such affairs. In the US, Congress establishes specific objectives for trade negotiations which it permits the president to enter into. Parliament could seek to emulate such processes.

Failing this, we are back to October and a vote which is anything but meaningful. The concrete parts of the “deal” that parliament will have to sign off will concern the past and the immediate future – the withdrawal agreement and transitional arrangements. There is absolutely no prospect of a trade deal being negotiated by the autumn. The best that the government can hope to have achieved will be an article 50 agreement, a deal on transition and a statement of intent (“heads of terms” in the jargon) on trade.

Of course, the EU may well refuse to sign off on the kind of obviously contradictory statements the prime minister is fond of making (leaving the customs union and single market, combined with frictionless trade). Yet that leaves plenty of scope for ambitious, woolly language.

MPs will not have much to go on, so the vote will, in practice, not be about the actual text of the withdrawal agreement but a decision to reject the government’s entire approach to Brexit and start again. Voting the bill down would be what Portes has labelled the “Samson option” – triggering unpredictable consequences ranging from an election to another referendum or even a new coalition government. As Matthew Goodwin has argued, there are good electoral reasons as to why the Tories should support what he chooses to refer to as a “real Brexit”. And even some diehard Conservative remainers will balk at the idea of voting in such a way as to make a Corbyn government more likely.

Nor is there much evidence of the kind of public pressure for a reconsideration of the 2016 referendum that might give potentially rebellious MPs heart. As John Curtice has recently shown, insofar as there has been a shift in opinion over Brexit itself, this has been more “abgret” – people who did not vote in June 2016 declaring they would now vote remain – than “Bregret”, leavers changing their minds.

Moreover, while recent polling does indeed show increased support for a second referendum, there is no consensus over the form this should take. Michael Ashcroft has illustrated that support for another popular vote varies depending on what questions are asked. Excluding “don’t knows”, the only kind of referendum a majority favour is one providing a choice between the deal Theresa May secures and Brexit with no deal at all. On what could be called the remainers’ preferred option – a choice between the deal on offer and staying in the EU – those opposed to a referendum (42%) outnumber those in favour (40%).

However, assume that – all these potential roadblocks notwithstanding – we arrive at a vote that presents the British people with a choice between the deal on the table and remaining in the EU. It is far from given that this will generate a majority for the latter. The glaring inaccuracy of the short-term forecasts published by the Treasury immediately before the referendum has provided ammunition to those who would cast doubt on forecasts of Brexit-related economic damage. And increased pessimism about the economic impact of Brexit does not necessarily translate into strengthened opposition to Brexit itself.

But suspend disbelief yet again. Assume the outcome was, for the sake of argument, a 52-48% victory for “reject and remain”. What then? At EU level, this would doubtless spark a debate as to whether article 50 is revocable unilaterally, rather than with the approval of the European council. This is a question which has bitterly divided lawyers, with those believing in unilateral revocation disproportionately based in the UK.

Finally – one last effort here – assume even this is sorted out. MPs have voted for a referendum with remain as an option. The people have opted to remain in the EU. The EU has allowed us to change our minds. Does anyone really believe this will settle the question once and for all?

Leave aside the questions as to what a reversal will do to trust in government and politics in general among leave voters. Leavers would not simply accept the result and give up. Rather, we would confront something akin to a political groundhog day. We would wake up to Ukip polling well above 20%. To the Conservatives hopelessly divided and held to ransom by Brexiters. To Labour triangulating, attempting to hold on to both pro-Brexit and pro-remain seats. Amid the bitterness and the rancour, we would poison the EU from within, while the debate at home rages about the need for a definitive vote to settle the score.

Remainers are, of course, entitled to try whatever they can to secure the outcome they want. But we should be frank about the numerous, often formidable, hurdles standing in the way of a reversal of the referendum result. And we should be honest about the significant problems such an outcome would generate.

• Anand Menon is director of the UK in a Changing Europe and professor of European politics and foreign affairs, King’s College London. Join him and Dan Roberts, Brexit policy editor, and Anne Perkins, deputy politics editor, at a Guardian Live event on Tuesday 13 March, Newsroom: Halfway through Brexit