The central claim:
The powerful GMB, Unite, Unison and CWU unions held covert talks in London soon after the General Election ... A source at the meeting told The Sun: "It was a carve-up. They all agreed to endorse whoever could stop David winning."
Except that they did not endorse the same candidate - with the CWU nominating Ed Balls, which does rather seem to destroy the central point of the "plot".
(Nor do The Sun mention other unions endorsing other candidates: Usdaw and Community for David Miliband; Aslef and TSSA for Diane Abbott; while Ed Miliband also has the support of the NUM, UCATT and Unity).
The Sun complains the CWU nomination for Ed Balls was despite a poll showing David Miliband in the lead with their members. So what can their members do about that? Perhaps The Sun might then have mentioned the good news too that what counts in the ballot is how union members cast their individual votes for the candidate they want.
So Tony Blair won 52% of the union first preferences in the last leadership election in 1994 against the pattern of union endorsements for John Prescott and Margaret Beckett.
The individual ballots are a great improvement on the electoral college when Neil Kinnock and John Smith were elected. Union endorsements and bloc votes gave him 97% of the affiliated section. Official union endorsements for any candidate don't count for anything in the electoral college without hundreds of thousands of individual trade unionists choosing to cast their own vote for or against recommended candidates.