There are roughly three positions within British politics on Brexit: quit everything European in order to strike free trade deals with the rest of the world; stage a new referendum in order to reverse the Brexit process; or mitigate the impact of leaving the EU by staying as close its regulatory principles as possible or necessary.

This latter position commands a majority in the House of Commons, has the technical support of both frontbenches and, as far as we know from the polling, the British people. It is also the right position. But Theresa May’s inability to turn that position into legislation - or even into a coherent negotiating strategy - looks increasingly likely to bring her down. She has scheduled a marathon one-day voting session in parliament on 12 June, during which she will attempt to overturn all 15 amendments from the House of Lords to the Brexit bill, including - crucially - the commitment to staying in a customs union.

This commitment would kill de jure the right-wing Tory dream of independent trade deals, which has died de facto as May has retreated from hard Brexit rhetoric. That’s why May’s team has made it a do or die issue when, on almost all other aspects of the Brexit plan, they have moved closer and closer to mirroring the regulations of the single market.

For Jeremy Corbyn, the opportunity is there not just to defeat May on a customs union, which Labour supports, but to shatter the authority of her government and reset the terms of the Brexit negotiations. But the cards need to be played with care and dexterity.

For starters, Labour needs to tone down its tribalism on the customs union issue. There are up to 15 Tory rebels prepared to uphold the Lords’ decision. Even if a few die-hard Lexiteers on the Labour benches vote with the government, that’s enough to inflict defeat. Labour should impose a three-line whip on the customs union vote and make this - and only this - the issue of the day. It’s not just about standing back and letting Anna Soubry or Dominic Grieve grandstand for a few moments: it’s about Labour itself embracing the national interest argument for a customs union.

First, only a customs union can cement the Northern Irish peace deal. Second, by seeking a customs union with the EU, Britain will have made its first conciliatory gesture in the entire proceedings - a gesture which the Foreign Office could exploit to remove blockages and tensions over security co-operation and the Galileo satellite system. Third, only a customs union guarantees the future of the auto, aerospace and energy manufacturing plants that have become the high-value core of British industry.

Fourth, remaining in a customs union with the EU will be a major geopolitical commitment. It says that, at a time when Donald Trump is starting a trade war against European steel and when Vladimir Putin is trying to dismember Nato, we have chosen to be part of the closest, biggest and most congruent economic trading and security partnership in the world to Britain, despite its flaws.

One of the reasons Labour’s tribal instincts have been awakened is that, since the 2017 general election, a small section of the neo-Blairite right have been signalling their willingness to form a new, pro-Remain centrist party, by taking part in cross-party initiatives with Anna Soubry et al at every opportunity. It looks like, and is intended to look like, a massive “up yours” to the party membership and is going down badly even in traditional Labour right-wing circles.

The same Blairite figures are busy agitating for a second referendum, for remaining in the EU, and for an unconditional application to stay in the single market after Brexit - an agitation currently focused around supporting the Lords amendment to stay in the European Economic Area (EEA).

These positions are rightly rejected by the majority in Labour, but on this occasion, the Labour frontbench needs to be seen to do what the Blairites have been pretending to do: unite the centre of British politics around a clear decision in the national interest.

Once May’s authority is shattered she may get overthrown, or might limp on until the Conservative Party conference in October. But that, in turn, poses Labour a challenge it has been unwilling to meet so far. Keir Starmer’s six tests for the “meaningful vote” on a government Brexit proposal would, once May is gone, be pretty irrelevant.

We’d be in a situation where it was clear no Tory government is ever going to propose a coherent exit plan that could be judged against the tests themselves. May has already conceded that test number two - does it ensure the “exact same benefits” as being in the single market – will not be met. Test number six, on being fair to all nations and regions, cannot be met under conditions where Whitehall is recolonising both Scotland and Northern Ireland. Test number five - does it defend national security and international crime-fighting capability – is going up in smoke as the EU plays hardball.

In a situation where the government is in freefall, “tests” are not enough. You need concrete policies. And the reason Labour has shied away from outlining them is clear. The only way you’re going to get the benefits of the single market is by either being in it, or so aligned to it that you might as well be in it. That’s why I’ve advocated, from the very day after the referendum, that Labour fight for conditional entry into the EEA via the European Free Trade Association (EFTA).

The conditions would – if we are to believe the Remainers – not be hard to meet: as Corbyn outlined on 2 February, Labour would need assurances that its plans on state aid, nationalisation, outsourcing and a state investment bank would not be challenged within the single market. Despite the repeated assurances of academics, Brussels negotiators themselves have been prepared to brief to the contrary.

If such assurances can be gained that would leave the issue of migration. Here, again since day one, I’ve advocated that Britain join EFTA/EEA and use Article 112/3 of the EEA Treaty to request a temporary “emergency brake” on freedom of movement, until a Labour government can alter the dynamics of the UK labour market to deter the exploitation of migrant labour, and reconfigure public services to meet the demand placed on them by unpredictable arrivals from the EU.

Having outlined the need for a “strong relationship” with the single market in February, Corbyn’s frontbench has veered away from it because Chuka Umunna and various remnants of Blairism have been trying to bounce the party into unconditional support for the single market. The TUC is meanwhile pushing Labour not to rule out single market membership.

As a result, in inner-party circles, being for or against the single market has become shorthand for all other enmities. When, as they should, Labour whips MPs against supporting the Lords amendment on the single market, these enmities will reach a peak.

Corbyn supporters, including myself, suspect that the Blairite rump wants to commit Labour to an outright Remain position not just on principle, but so that it can lose the next election by losing its northern/midlands and Welsh valleys base, and so that normal neoliberal service can then be resumed inside the PLP.

But in the next seven days, the art of being Labour is to refuse to get worked up about Umunna, Anna Turley and their rumoured new parties, and to get worked up, instead, about the possibility of - as Arthur Greenwood did in May 1940 – speaking for Britain and bringing May’s shambolic administration to a close. For that Labour needs more than just discipline. It needs to outline a vision that goes beyond “tests” laid down for a government that no longer exists.

On the day after May slinks, leaden-faced, from defeat in the Commons, Labour needs to produce its own white paper on single market membership, and to ask the progressive nationalists, the Greens and the Lib Dems to support it. It should contain conditions: a clear intent to place a floor, not a ceiling, on social and environmental rights, and a request to suspend freedom of movement temporarily while signing up to the principle.

Does that go further in a pro-EU direction than critics like me would like? Yes. If I could design the EU from scratch I would do it without free movement, without the euro and with much tougher enlargement rules, most of which countries like Hungary and Croatia would not meet.

But, as Britain’s former EU ambassador Ivan Rogers pointed out three weeks ago, the EU is a regulatory superpower and all sensible options for Britain once outside it involve mirroring single market rules to gain market access. In return for compromising over the downsides of the single market, Labour gets its upside: the regulatory floor on employment and environmental rights that causes the Tories to want hard Brexit.

If the EU refuses these conditions for EEA membership, the fallback option should be a Labour version of close regulatory alignment. None of these outcomes solve the problem of "rule-taking" but that is a problem created by the referendum result, not Corbyn.

If Labour can bring itself to make a clear proposal on conditional EEA membership, the ball would then be in the court not only of Michel Barnier but of Chuka Umunna, Alastair Campbell and George Soros: here is Labour actively fighting for a European future that, at the same time, respects the wishes of the 17 million people who voted to leave the EU. “Are you with us or against us?” would be a much more powerful question to those plotting a centrist breakaway if Labour were prepared to replace its tests with clear proposals.

Electoral support for Corbyn’s Labour has been largely resilient (though at times this year it has been on the ropes). The next seven days are the moment for Labour to come out of its corner, landing hard (metaphoric) blows on the xenophobes and Little Englanders of the Tory right. For that, it needs its left jab and its right hook aimed at the same target.