The name Beesley Shotover was unfamiliar to me, but this article enlightened me: The photographs of the locks should be pretty useful in analysing the mechanism. There is also a discussion of it in Burrard's "Modern Shotgun".
Beesley Shotover
I once owned a Westley Richards Ovundo in caliber 400/350, with hand detachable locks, but sold it due to the unavailability of the 310 grain bullets for which it was regulated and which John Taylor was so complimentary of. Also, my Krieghoff "Teck" over and under .375 H&H made the caliber somewhat redundant.