Every Wednesday morning in the House of Commons, about a dozen people can be seen making their way along the committee-room corridor to attend a ‘grassroots co-ordination committee meeting’. Before they get down to business, the group, a mix of MPs and campaigners, are treated to a monologue from their meeting chair, Labour’s Chuka Umunna. This speech varies but the agenda is the same: how to bring about a second referendum and stop Brexit.

The ‘Stop Brexit’ campaign has taken many forms since the referendum result two years ago. There have been legal challenges, a surge of anti-Brexit campaign groups and plans for a new party — not to mention the one-man nationwide tour from Lord Adonis. He didn’t say that much on Europe before the referendum. Now, however, for him, as for so many others, passion for the cause arrived only after defeat. Cash is flooding in to the various campaigns, unregulated by any election watchdog.

At first, Brexiteers watched their antics with a kind of schadenfreude: look at the sore losers. But now things are getting a little more serious. A second referendum might be unthinkable, but wasn’t the same once said about Brexit itself?

The efforts, so far, have been fairly disorganised due to a reluctance among the various anti-Brexit groups to work together. ‘It’s all been a bit People’s Front of Judea and the Judean People’s Front,’ one organiser explains. ‘Each group thinks they know a bit more and there’s also the fact that some people are more into promoting themselves.’ Talk of a new centrist pro-Europe party organised by Simon Franks, the founder of LoveFilm, has left many lukewarm. ‘They say he’s got £50 million behind it. I’d be surprised if it’s even £5,000,’ snipes a rival centrist.

One cause most Remain activists can unite around has been found in the so-called ‘People’s Vote’. Launched in May, it has a simple proposition: give the public a say on the final deal. More facts have emerged since that original referendum, it is said, so there should be a second vote. For the first time, the various grassroots Remain organisations — nine, at the last count — have come together behind a single message.

Those involved are suddenly feeling more optimistic than they have in months. Since Theresa May’s Chequers Brexit compromise has been denounced by Brexiteers and Remainers alike, the chance of no deal may have risen — but so, they say, has the chance of no Brexit. Just this week Julian Dunkerton, founder of the Superdry retail chain, donated £1 million to the campaign and announced that he had ‘a good instinct for when a mood is going to change and we’re in one of those moments now’.

They are targeting a ‘mushy middle’ of the electorate. Message-testing earlier this year found that the phrase ‘people’s vote’ appeals to soft Leavers and soft Remainers. People who mistrust Brexit stories on either side have switched off. ‘People have PTSD on Brexit now,’ said a voter in a recent focus group. Campaigners think such people will come off the fence only once they see what May comes back from Brussels with in October. This is when the polls ought to shift.

So a plan has emerged, with three main parts. The first is to persuade Jeremy Corbyn to drop opposition to a new referendum. We can expect a move to be made at the Labour party conference next month, perhaps a motion called where members will seek to force the leadership’s hand. This was stopped last year, but the mood has changed and some pro-Corbyn Momentum figures now support a second referendum. Even if the party doesn’t go the whole hog, it could be forced into adopting a compromise that would make a second vote consistent with Labour policy.

The next part is to woo Labour MPs. Most back Remain, but often out of deference to their constituents, say that they consider the matter closed. Now about 20 or 30 Labour MPs are thought to be open to persuasion — such as Caroline Flint, Gareth Snell and even eurosceptic Dennis Skinner.

The third part, perhaps the hardest, is a charm offensive to Tories. The likes of Anna Soubry, Sarah Wollaston and Justine Greening have already come out in favour of a second referendum but up to 20 more Tories are seen to be susceptible. They tend to be the MPs who have flirted with Brexit rebellion previously like Heidi Allen, Paul Masterton and Nicky Morgan.

With enough MPs, the aim is to pounce when the final deal comes to a vote — perhaps in October or November — at which point rebels could insert a motion proposing a new referendum on May’s deal. It would be at the discretion of Speaker John Bercow to decide whether to force a vote. The greater the cross-party support, the more chance of Mr Bercow permitting it. ‘It’s worth a shot, it might just work,’ explains a figure involved in the planning.

The Eurosceptic backlash is seen as key to the Remain end goal. If the Tory Brexiteers, led by Jacob Rees-Mogg, try to sink May’s Brexit plans, as many as 80 Conservative MPs could refuse to vote it through. That would put more power with the People’s Vote backers. ‘We would say “we’ll vote for this if you adopt the amendment”.’

There are many reasons that the plan might fail but some of the Remainer supporters have taken to talking as if victory is within sight. Lord Adonis said that after parliament votes to stay in the EU he would like to join ‘a large parliamentary delegation travelling to Brussels for that purpose, followed by the greatest party ever’.

But is this democracy in action or more just the manoeuvres of a disgruntled elite? ‘It’s all very Westminster right now,’ sighs one campaigner, who worries not enough has been done to change the public mood. Much of the force behind the Brexit vote came from people who felt they had become an afterthought. The People’s Vote might have its parliamentary strategy all sewn up, but it ought not to forget the people. Otherwise, even if the Remain side gets the second referendum it craves, it might not get the result it expects.

The People's Vote campaigners are targeting a 'mushy middle' of the electorate

SPECTATOR.CO.UK/COFFEEHOUSE Hourly updates from Parliament and beyond.