Founded in 1949 as Associate Dairies and Farm Stores Limited, the present name is derived from their amalgamation with Asquith Supermarkets in 1965 (Asquith and Dairies).
There seem to have been many changes in the structure of the organisation since then - the dairy division was sold and is now known as Associated Fresh Foods - at the present time though it is owned by Corinth Services Limited, a subsidiary of Wal-Mart.
I quote from the Pevsner Guide to Leeds
"E of the bridge is a path along the river's s bank lined by the tedious, long low three-storey brick range of the Asda Headquarters, 1988 by John Brunton Partnership; one of the first commercial developments in this run-down area. Quasi-traditional, with an unnerving variety of window forms including canted oriels rising to gablets and a clerestory under deep eaves."
I don't think the author is over-impressed but Barbara Hebden did a fabulous job on the embroidery - hand stitched on printed fabric, including french knots.