Edit - I may have made a boob when measuring - I measured the total length, it may be the case that the length measurement is between the screw holes. Any advice appreciated.
It's a very popular make. The link opens ironmongery direct with all their union products. If you can find the lock+plate combination you have a chance of getting the plate on it's own.
They usually come as part of a set. Does the lock body have a manufacturers name?