Jeremy Corbyn’s supporters are celebrating a clean sweep of Labour’s internal election for places on the party’s National Executive. All nine places elected by party members went to candidates on the slate organised by Momentum, the leader’s fan club.

It was an impressive result but also consistent with the idea that we have passed Peak Corbyn. The share of the vote won by Momentum candidates was down from last time, and Eddie Izzard – standing as an independent, non-factional celebrity – came within a whisker of winning a place. He came within 2,500 votes of the 70,000 won by the lowest placed Momentum candidate, Peter Willsman.

Willsman was re-elected despite being dropped from the Momentum slate four days after the voting started, when the recording of him at a National Executive meeting was made public. In it, he ranted against rabbis falsifying examples of antisemitism in the Labour Party – but, by the time the recording emerged, many people had already voted.

What the results also showed was that non-Corbynites still attract a large minority of the votes. Two years ago, when Corbyn won his second leadership election, Owen Smith, his challenger, won 38 per cent of the members’ vote. Since then many non-Corbynites have left the party and yet it seems they still make up a quarter to a third of the membership.

Corbyn supporters will accuse me of clutching at straws – and that is exactly what you would expect a Blairite to do. But they might also realise how hard it will be for them to keep up their enthusiasm for another three years.

Of course, it is better from Corbyn’s point of view that he has kept his grip on the National Executive. He will need it this afternoon when it discusses the plan to adopt the International Holocaust Memorial Alliance definition of antisemitism, with all its examples in full but also with a codicil confirming the right of Labour members to criticise the government of Israel. Momentum’s decision to fudge its position on a final say Brexit referendum at Labour’s annual conference in Liverpool at the end of this month may also be helpful in getting over that awkward bump.

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But victory brings pressure to secure further advances, and that starts to take Corbyn into more difficult territory. His supporters’ control of the National Executive means that plans are likely to go ahead to make it easier to deselect non-core-group Labour MPs. This is more exciting to many Momentumites than having to decide their position on Brexit, but it is a double-edged sword. They think the media are biased against them anyway, but the one thing that would guarantee damaging headlines for Corbyn would be a series of internal battles between now and the next election to get rid of Labour MPs. Some of them may (unlike Frank Field) resign to fight by-elections, and if they are popular enough locally they might even win them.

Internal party democracy is mostly just a slogan for factional advantage, although the case for easier deselections is strong. Party members ought to be allowed to choose parliamentary candidates who would at least be prepared to say they want Corbyn to be prime minister.