Meanwhile give that magneto slip ring a good clean. Carbon deposits tracking round can produce uneven running. Pick up brushes also need to be clean, free and of good quality. Some available are softer than a kid's pencil... Useless.
Weak mixture can also cause spitting back, air leak at carb joint a favourite, sticky inlet valves also worth a look but worn inlet guides and worn throttle slide also suspects. BSA Service Sheet 708 tells all.
Stuck clutch....Hooligans trick is to start as normal, then get bike moving down a handy slope and kick into second gear with the clutch lever pulled in. Then taking your life in your hands try blipping the throttle and with luck the changing loads will free the plates.
Swarfy.