Unison, regarded as the "swing vote" among Labour's trade union affliates, has endorsed Jeremy Corbyn for the Labour leadership.

The endorsement is a blow, but not a surprise, to Yvette Cooper, who at the beginning of the campaign had expected to secure the backing of the largely public-sector body. But any hope of that Cooper would pick up the endorsement had long since faded, with aides briefing weeks back that the endorsement of Unison - and the GMB, who have decided not to endorse - was no longer on the cards.

The development is still something of a shock within Labour circles, not least because, behind the scenes, Unison used its not inconsiderable muscle to secure early endorsements and nominations from MPs for Cooper. But it is more significant because, while Unison is smaller than Unite, it is regarded as representing the centre of the Labour party. "Unison is us," one MP once remarked to me: public sector, soft-left, not antagonistic towards the New Labour era but not nostalgic for it either. It was Unison's switch from Ed Balls to Ed Miliband that convinced several MPs to hand their votes to Miliband, which proved crucial to his narrow victory. (Of the two more centrist trade unions, Community has backed Cooper while Usdaw, the shopworkers' union has opted for Andy Burnham.)

What's going on? I'm told that Balls' support for public sector pay freeze as Shadow Chancellor had soured several senior members of Unison towards the idea of a Cooper endorsement to begin with, but there was still a great deal of goodwill towards Cooper, who has long cultivated her relationships with Unison. It was Cooper, too, who made much of the early running against a continuation of the pay freeze in this year's budget. But the emergence of Corbyn, who has been even more strident in his opposition to cuts to the public sector, as a credible contender for the party leadership strengthened the hand of the anti-Cooper bloc.

But the most significant part of all is that even those unions who are seen as moderates are now supporting the Corbyn campaign, highlighting just how much Labour and its affliates have changed since 2010, and why Corbyn's chances of securing the leadership are as good as they are.