Brexit talks have started. Parliament embarks on two years of legislative Brexit blood, sweat and tears. But amid the rancour, the unreported story is the frighteningly cosy consensus on Brexit between Theresa May and Jeremy Corbyn.

The chatter is all about cabinet splits and the revival of the Conservatives’ 30 years’ war over Europe. But what of the confused position of Labour? The party could be mobilising effective opposition to a hugely harmful hard Brexit, yet contradictions abound. Spokespeople attack this hard Brexitm but then sign up to leaving the customs union and single market, which is in essence what hard Brexit means. Others, including Sadiq Khan, argue that the party should campaign to stay in the single market.

Labour was brilliantly successful in the election at mobilising young people, who were angry that their European future had been stolen from them but who perhaps didn’t scrutinise the small print in the manifesto. Before long they will. They may not know that Jeremy Corbyn ordered his troops into the division lobbies to support the extreme Conservative-Ukip Brexit, but may now notice his insistence that Brexit is “settled”. Make no mistake, on Brexit Corbyn is betraying many who followed him.

Seen from outside, there appear to be two factors that have turned Labour away from the strongly pro-Europe party of Neil Kinnock, Gordon Brown and Ed Miliband.

The first is the dated, 1970s doctrine that Europe is a wicked “capitalist club”. Except in a few dwindling bastions of the French Communist party (the bits that haven’t defected to Marine Le Pen), there is no serious leftwing party in Europe still clinging to that view. Yet it is a powerful influence at the top of the Labour party, even though from workers’ rights to environmental protection, it is Europe that best guards our progressive ideals.

The other influence is more practical: the belief of MPs in seats where a majority voted for Brexit that they were compelled to defer to their constituents, especially over immigration. Otherwise they ran the risk of being devoured by Ukip or the Conservatives. With hindsight, that fear was exaggerated. Indeed, Lib Dems won seats that were strongly Brexit. As someone who won a strongly remain constituency, I understand the dilemma. Yet it is far from clear why this would lead Labour to want to scrap the customs union, which is fundamental to the business model of many manufacturing firms with EU supply chains. Hopefully Labour will see (belated) sense on that issue.

A trickier issue is the single market, because of the belief that its “four freedoms” necessarily entail unrestricted immigration from eastern Europe. I have a liberal view of immigration, and I certainly subscribe to the principles of the single market (and, like my Labour predecessors in government) sought to promote and deepen it.

You can’t say often or loudly enough that Britain has benefited hugely from immigration economically, socially and culturally. But I do understand why people, especially those at the economic margins, are concerned about immigration,and that raising these issues is not proof of bigotry. Labour’s shame is to effectively align themselves on Brexit with a party (the Conservatives) that has no interest in tackling housing, training and lack of investment. These are the problems that drive a lot of resentment about immigration, and they are problems made in Westminster, not Brussels. We need to call out May and Corbyn every time they gloss over this inconvenient truth.

Both May and Corbyn are putting ideological purity before common sense

But even if you believe that the sheer number of migrants needs to be addressed, that still does not hand May and Corbyn an excuse to leave the single market and customs union. Both leaders are putting ideological purity before common sense. Some of the most committed members of the EU allow exceptions to free movement. The Germans do not accept professionals who do not meet German standards: one reason why we are far from having free trade in services.

There are mechanisms by which Britain could remain within the world’s most lucrative single market while applying national measures to limit EU migration, such as by restricting admission to those with a prior job offer or qualifying the right to search for work. These possibilities could have been better explored before the referendum, but we start from the current mess.

Labour should look afresh at Brexit so that it can work with other opposition parties and Conservative dissidents in the new parliament. If it does not, it will be complicit in a massive act of economic self-harm, voting to make Britain poorer and impoverishing our public services. Its new young supporters will soon notice – and Corbyn’s halo will surely slip.