The main Blackburn factory was Brough, still operated by BWoS. It was located there, because, being next to the Humber, it could have a slipway for the seaplanes, which were the core of their activities in the '20's. Before that they operated from the Olympia works in Leeds, which later became an icerink, and then in the '80's was knocked down to become a Tesco :-(
BWoS still operate that sole remaining B2, although I don't recall having seen it for a few years.
As was said above, the London operation was probably a shadow factory. Although, like most aircraft manufacturers in the '20's, Blackburn did have a sales operation in London.
It is fair to say that most of their products in the '30's were mediocre, but the Skua did record the first British kill in WW2. And the Bucc had an extremely successful career, and was loved by most of its aircrew, as a look on the Military forum will attest.
regards
Skua