So with a little more digging into the Belgium and British proof marks:
The format of the Belgium Marks on the barrels span 1910-1924 and there is a "C" stamped on the action in two places, which donates 1924 as the manufacturing year.
The London proof marks span 1924-56 which would JUST also tie in for a 1924 date... But I've got no further along with a manufacturer...
The unusual logo (Possibly J and R in a circle) and the JW on the barrels are, I think, the only thing left to go on... I've been through the list of Belgium firearms companies that I can find on littlegun.be but not got any further at this point.