They met for lunch in the Drapers Arms, one of London’s top gastropubs, just a few yards from Emily Thornberry’s constituency office in Islington.

After 90 minutes, says Ken Livingstone, it was clear that he and Labour’s new defence spokesman didn’t disagree on anything. And, in particular, they both thought it would be wrong for Britain to renew Trident, as the government plans to do, and which is still Labour party policy.

Livingstone told Channel 4 News this afternoon: “At the end of an hour and a half I just said, ‘Look, you and I agree on absolutely everything. I think you should lead on this. You’re our defence spokesperson. You’ve got to explain it in parliament and at the next election, so I’m delighted’.”

That, at least, is how Ken Livingstone explained to us today’s announcement that he’ll let Emily Thornberry chair the Labour party’s defence review on her own, without his involvement. Had Maria Eagle still been shadow defence secretary, he says, it would have been very different, since Eagle is pro-Trident. Livingstone would have stayed on as co-chair, he says. But it would have been a long slog – “trench warfare”, in his words. He and Eagle would have argued over every detail, and every line.

Yet only two nights ago Ken Livingstone told BBC Newsnight that the defence review (which he still claimed to be running jointly with Thornberry) should be able to come up with its conclusions on Trident within two months or so.

“We will desperately try and do it as rapidly as possible,” he told Newsnight. “So we will focus on the Trident issue ahead of the rest of the defence review … With a bit of luck that can be done in eight to 10 weeks. It will take a lot of work for me and Emily, but that’s good.”

Those don’t look like the words of a man who has decided to stand down from running the review. What’s more, Thornberry now looks to be working to a much slower timetable than Livingstone envisaged on Wednesday. Thornberry today formally invited people to make her submissions to her review, and announced a deadline of 30 April. And she says she might be able to issue an interim report on Trident by about June.

That’s crucial, since the government is likely to hold the big Commons vote on Trident in March or April, too early for Thornberry’s interim report, though she claims her review will already have gathered important information to help Labour MPs in the debate.

Livingstone’s departure makes it less likely that the review will come out against Britain’s membership of Nato, which he said last week would be covered by the party’s review. Jeremy Corbyn has opposed Nato membership in the past (though his office quickly slapped Livingstone down on the Nato question last week).

His stepping down from the defence review, and the adoption of a slower timetable, will no doubt come as some relief to the two big Labour party unions, Unite and GMB, who represent workers who will be making the new Trident submarines in Barrow. Both unions are pro-Trident and there would have been a big bust-up had Jeremy Corbyn tried to change policy on Trident without a decision by the Labour party conference.

It’s a very tricky issue for both unions, since they are competing for members in Barrow. And in the case of Unite, its leader Len McCluskey is personally opposed to Trident (along with a majority of his executive), but he insists his foremost duty is to represent his members.

Now both sides are left reasonably happy. Labour will eventually emerge, no doubt, with a new anti-Trident position, to be endorsed perhaps at the Labour conference next autumn, or the following year, 2017.

One long-standing expert on the left predicts the conference (where half the votes come from the unions and half from the constituencies) is likely to go somewhere between 60-40 and 55-45 against Trident. In the meantime the government, of course, will have gone full speed ahead with the big decision, which will keep Unite and GMB members happy in Barrow.

In the shorter term, however, Ken Livingstone still has a role in Labour’s policy-making process as co-chair of the party commission on Britain in the world, in conjunction with the shadow foreign secretary Hilary Benn. Indeed the defence review officially reports to the Britain in the world commission, and if Hilary Benn tried to oppose a new anti-Trident policy no doubt Livingstone would be ready to engage in the kind of “trench-warfare” he expected with Maria Eagle.

Remarkably, a source close to Hilary Benn says nothing has actually changed, in fact, and that Livingstone never was co-chair of the defence review in the first place. That was always run by the shadow defence secretary, he claims, be it first Maria Eagle, or now Emily Thornberry. “I think he’s just confused,” the source says.

So, too, are the rest of us.

The Commons debate will be very tricky for Labour, but that would be true whatever happened, since Labour MPs are badly divided on Trident. Jeremy Corbyn’s best bet is probably to allow his MPs a free vote on the matter, only unlike the Syria debate last autumn, we won’t see the absurd spectacle of Jeremy Corbyn speaking one way, and his shadow cabinet spokesman speaking the other, as happened with him and Hilary Benn in the Syria debate. This time Corbyn and Thornberry are likely to speak in the same direction.

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