Today the Liberal Democrats have moved from being a party supporting a second referendum on EU membership to one that simply wants parliament to revoke article 50 at the earliest opportunity. This type of polarising behaviour mirrors the no-deal extremists on the other side of the debate and illustrates exactly why British politics is stuck in deadlock.

Jo Swinson’s decision is nonsensical for two reasons. First, it flies in the face of everything the party has ever stood for. How can any Lib Dem politician look their constituents in the eye, refer to themselves as a “democrat” and then pledge to overturn the biggest democratic exercise this country has ever seen, without even having the courtesy to first ask the public if they have changed their mind? It is as astonishing as it is hypocritical.

Second, it completely misunderstands how most people in the country feel about Brexit. Of course, some remain voters want to stop it at all costs. But they really are a tiny majority, despite what Twitter may lead politicians to believe. There is a far more sizeable chunk who are convinced that, because of parliament’s failures thus far, a second referendum is the best way out of this mess. I do not agree with this position, but I have sympathy with those who have lost trust in parliament to deliver.

What the Lib Dems and other hard remainers miss is that there is a sizeable majority of the public, consisting of both remain and leave voters, who just want parliament to get on with it. They might not accept any old deal – many were far from impressed with Theresa May’s initial “blind Brexit” that was voted down three times – but they do understand that we need to find a way out of this quagmire. They recognise that consensus and compromise are not dirty words, but are in fact the lifeblood of any liberal democracy.

Fortunately, a solution is staring us in the face. After May’s deal was rejected a third time she belatedly reached out to the Labour leadership and began cross-party talks. The discussions broke down, but on 21 May, the then prime minister announced several compromises. These formed the basis of the withdrawal agreement bill (Wab): they included a pledge on workers’ rights, a vote on a customs arrangement, a role for parliament in future UK-EU trade talks, and even a vote on whether to put the deal back to a confirmatory public referendum. Labour fought hard to win these concessions, and it is an absolute travesty that MPs were not allowed to debate, or even study, the bill.

So today Caroline Flint, Rory Stewart, Norman Lamb – a Lib Dem disappointed by his party’s change of policy – and I launched our MPs for a Deal group, calling on the prime minister to recognise that the Wab is a strong basis for a Brexit deal. Why would he ever resurrect a version of a deal he has repeatedly criticised? Because his options are very limited. He is legally bound to ask the EU for an extension on 19 October yet he says he would “die in a ditch” before doing so, giving him only three routes forward. He can simply break the law by not requesting an extension. He can resign. Or he can pass a deal. Tabling a version of the Wab is by far the most likely option for securing a majority.

I really hope more Lib Dems join our cross-party group and understand that their bid to revoke article 50 polarises the debate even further. I also hope my own party recognises that it is in the national interest to back a deal.

It is easy to forget that the vast majority of MPs have voted for a Brexit deal of some kind or another, and that securing one is the most popular way forward. But for far too long our parliament has been paralysed by the extremes. Enough is enough. We must now break the deadlock. It’s time to rediscover the lost art of compromise.

• Stephen Kinnock is Labour MP for Aberavon, a member of the select committee on Exiting the European Union and a member of MPs for a Deal