As soon as Ed Miliband was elected Labour leader in 2010, political commentators argued he had only won because of the 'union vote'. (In the final round of voting, Miliband won 46.6 per cent of MPs’ votes, 45.6 per cent of party members, and 59.8 per cent of affiliated union members.) The line was repeated over and over by Tory frontbenchers. In 2013, David Cameron told Miliband that the unions 'own you, lock, stock and block vote', even though John Smith had abolished the union block vote in 1993.

As soon as Jeremy Corbyn was seen to have a chance of succeeding Miliband, the argument was rehashed. In the Telegraph, Toby Young said the unions would 'install' Corbyn as leader. Last week’s Panorama focused on the jubilant mood of Len McCluskey, Unite's general secretary, at the Durham Miners’ Gala, one of the first rallies at which Corbyn was seen as a credible contender. According to today’s Telegraph, 'Union bosses have threatened to use Jeremy Corbyn’s victory to cripple Britain.'

As Cameron’s 'block vote' jibe suggests, the people pushing this view are unlikely to let the facts get in the way. But the figures paint a very different picture. Under the new 'one member, one vote' system for electing the leader, introduced by Ed Miliband following the Falkirk selection debacle, an individual trade unionists’ vote counts as much as an MP's, a party member's or a registered supporter's. And union members had to opt in to receive ballot papers. Almost three million union members were eligible, but only 148,192 asked for a vote and 71,546 cast one, compared to 211,234 last time. Union members made up 68 per cent of the people who voted for Miliband; the figure for Corbyn was 16.4 per cent.

In the final round of the deputy leadership election, Tom Watson secured the support of 46.5 per cent of party members, 51.8 per cent of registered supporters and 52.1 per cent of affiliated trade union members. Corbyn’s figures for members and trade unions – 49.6 per cent and 57.7 per cent – were not far off. But he secured the votes of 83.8 per cent of registered supporters, who paid a one-off fee £3 to get to vote. After fears of entryism were raised, the party centrally more or less gave up on trying to bring in registered supporters. Of the four leadership campaigns, Corbyn’s was the only one whose website had a prominent link to the sign-up page.

Writing for the Blairite group Progress in 2011, Luke Akehurst stressed the need 'to promote the new registered supporters scheme in every piece of material we put out'. Labour’s right wing hoped the new influx would undermine the influence of trade unionists in the party. Saturday’s result suggests that it has, though not in the direction the Blairites wanted. Still, the trend isn't good news for the link between the unions and the Labour Party. In Parliament today, the Tories are pushing forward a trade union bill which – along with other anti-union measures that have led even the Conservative MP David Davis to make comparisons with Franco's Spain – will take Labour’s internal changes a step further. Trade unionists will be required by law to opt in to political funds. If a future leadership election under the unpredictable new system puts a 'moderate' in charge, Labour’s trade union link could be under greater threat than ever before – assuming the Tory government hasn't legislated it away entirely.