St Vincent de Paul Society. I've always called the St Vinnies but they've gone a step further and dropped the Saint.
I don't know what it was originally but it is good to see in still being used and well maintained.
Update - 19 March 2009
Thanks to a comment by Robin below and an article from the Herald 20 Nov 1940 which he has uncovered, I now know that the building was the Unity Theatre seating 500 and a lodge room built for the Manchester Unity IOOF as alterations and additions to their existing building and designed by architect Robert LePoer Terry. Thanks Robin, you're a star.
… back alley shipments! by James Vaughan
2 hours ago