The difference between the JAP 600 and the BJ magneto may only be the difference between a single cylinder engine (JAP 600) and the two cylinder British Junior. The mags will be the same but the points cover will be replaced on the BJ magneto by a distributor cap with a rotor arm inside.
The other thing to check is the direction of rotation- so long as that is the same you could most likely get a standard Wico A to work.