Mr McLeish joins other senior party figures – including ex-chancellor Alistair Darling, Scottish Labour leader Johann Lamont and ex-foreign secretary Jack Straw – in putting pressure on UK party leader Ed Miliband to reopen the inquiry into Unite, the party’s biggest donor.
Mr McLeish said: “The public, the Labour party and Unite members deserve to know what actually took place, so I would support an inquiry.”
He added: “We have to treat the public with respect and the only way we can do that – and I know it hurts and there may be difficult things to reveal – is to be transparent with them. There is a lot of public disillusionment. People think political parties operate in a different world.”
The controversy was at the heart of the recent crisis at Grangemouth. Owner Ineos threatened to close the petro-chemical plant after workers voted to strike over the company’s investigating Unite convener Stevie Deans about whether he used company resources to enrol members for Falkirk in order to fix the selection of Eric Joyce’s replacement as candidate for Falkirk West.
After a resolution was reached in Grangemouth, Mr Deans, who was chairman of the Falkirk West constituency, resigned ahead of publication of Ineos findings into his conduct.
Mr McLeish’s call comes as weekend reports of new e-mail revelations suggested Unite general secretary Len McCluskey is being investigated over election irregularities separate from claims his union tried to fix the Falkirk candidate selection.
It is claimed an inquiry has been launched after claims that Mr McCluskey’s own election included the balloting of 160,000 “phantom” members – similar to the claims made about the Falkirk selection. It has also been claimed voting papers were sent to deceased former members.
Jerry Hicks, who lost the election to Mr McCluskey in April this year, has demanded that the election is re-run. He claimed that 158,000 ballot papers were sent to members no longer paying fees between December last year and January this year.
According to Mr Hicks, Unite’s return for 31 December 2012 records 1,346,414 members with up-to-date addresses on the union’s system. The Certification Office, which regulates unions, is reported to have launched an investigation into the claims.
Mr Hicks’ representative, Jody Atkinson, said: “It appeared that Unite had been balloting people who had left the union, most likely because they had not paid their subscriptions. And it seems that ballot papers have been sent to people who have not been members for years.”
Mr Hicks insisted that he wants Unite’s leadership “to explain why people who weren’t members of the Unite union could vote in the election of its general secretary”.
Unite deny any ballots were sent out to ineligible members.
A spokesman said: “Mr Hicks has already been given a response on this matter by the independent Electoral Reform Services, which acted as returning officer in the election. The members referred to were in arrears and under rule entitled to vote in the general secretary election.”