Have you checked out the bikes of similar vintage at Classic Lightweights UK Reader's Bikes page? Since the frame has Campagnolo dropouts, a Cinelli (old logo) bar and stem would not be unreasonable, though I'd look for something British like GB bars and stem. Still, there's the Mafac angle, leading to a French connection -- I've seen French stems and bars that were 25.4 barrel diameter rather than their own 25 mm standard. The British were fairly eclectic about how they equipped bikes; they didn't have it all at home, and they seem to have been fairly value-conscious in their selections -- both reflections on their postwar economy.

There's a page on CLUK showing pre-war "Merlin" handlebars from 1939-40 -- don't know for sure if that was Bob Jackson, or someone else, and I'm pretty sure those were steel.