Don't expect too much of these depots... Often they were just that: a depot, where bikes were stockpiled. Believe it or not, Dudley Zoo in Birmingham was also a motorcycle depot during the war!
Shortly after the war lots of WD bikes were disposed off. The better ones were sold on the export market (this was the "export or die" period). That's how your Flea ended up on the other side of the planet...
Never knew that Dudley Zoo was used as a depot(Black Country though not Birmingham), there was a company in based in Dudley that boxed motorcycles for shipping abroad, SGB Ltd (Stourbridge Glazed Brick) I think they boxed Triumph 3HWs.
Ketley is only about 2 miles from the RAOC Central Ordnance Depot, Donnington, so it could have been an outlying store. It also looks as if there was an R.N. Armament Depot there located at the Wrekin Foundry. In the run-up to the liberation of Europe, any suitable buildings were used for storage.