Sawbones,
Until very recently, BA had two UK subsideries, Brymon, and British Regional (and Manx in the Isle of Man)- now they have joined together to become 'British Airways Citiexpress'- BA4000 were all previously operated by Brymon Dash 8's or ERJ145s, now BA citiexpress aircraft (if you get my drift) and this is the airline operating this flight (in full BA livery, with crew in BA uniforms etc etc.) Whether or not this counts as BA for you or not, I don't know, but on the surface everything is definately BA.
Sorry if that's confusing, but BA are a confusing airline!
All the best
G-BPEC