Well that front looks like a Bentley, so as there was a 1939 4¼ saloon body that looked rather similar, perhaps it was one of those.
The rear door seems too wide, but perhaps there was a long wheelbase version I haven't seen. Front of the front wings differs, but not an important matter, I'd say.
As Rolls Royce owned part of Park Ward from 1933 and all of it by 1939, probably one of their bodies.
I have no idea who might have built it.