The Manchester United manager, a former union shop steward and long-time Labour supporter, described the party’s candidate as “the only genuinely local candidate in this election”.
“ Willie understands what needs to be done,” Sir Alex said in his endorsement.
“Willie’s Action Plan for Glasgow focuses on people’s real concerns and priorities.
“His determination to crack down on crime and fight to improve chances for local people is spot on, and has my whole-hearted support.”
Voters go the polls on Thursday in the seat vacated when former Commons speaker Michael Martin quit during the expenses row.
Sir Alex added: “Glasgow doesn’t always get its fair share, so I know the value of having someone able to stop the city being ripped off.
“I always tell young players that being a footballer is the best job in the world.
“Yes, it’s hard work to reach the top, but it’s nothing to bringing up a family or running a household on a tight budget.”
Mr Bain said: “Sir Alex knows a thing or two about running a good campaign so I am delighted that he is backing us in the election.”
His intervention came as the SNP reacted to reports that direct East Coast Main:Line services between London and Glasgow are to end next year.
Responding to The Herald’s front page story on Saturday, the Nationalists claimed axing the service would remove more than 22,000 seats a week and more than a million seats per year from services to and from Glasgow, badly damaging business and tourist travel.
“This shocking news for travellers and business in the city came only days after the Labour transport minister and Labour’s candidate tried to lecture the SNP on the importance of direct rail services to the city” said SNP MP for Glasgow East John Mason.
“Labour’s hypocrisy knows no bounds.”
Lord Adonis, the Transport minister, was reported over the weekend as saying the rail service would not be axed, although meetings have been held between officials at the Department for Transport, Network Rail and other parties.
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