Russ If your bike is an A10 with an 18 tooth gearbox sprocket, it is either originally an A7 solo box or an A10 set up at some stage for sidecar work.
The boxes are the same inside, they have the same gears, but the rear sprocket would be 46 for an A7 solo, 49 for sidecar work. Standard gearing for an A10 is a 19 tooth gearbox sprocket, rear sprocket 42 teeth (solo) or 49 teeth (sidecar). However, owners could mix'n match because all the bits interchange.
The good news is that all these gearbox sprockets have the same spline, which is also common to the later Swing Arm box. These days 20 and 21 tooth gearbox sprockets are available for more relaxed less frantic cruising.
The scroll was changed to a seal sometime in 1951, this is the difference in your quoted A7 part numbers. All new sprockets are of the seal type, so you will need to fit the later seal, which is easily available and again common to all A series boxes, Plunger and S/A.
Like duTch says, the 5/16" refers to the width of the teeth, in other words wide enough to fit the gap between the sideplates of the chain, with a little bit of clearance. The rear chain size is known as 5/8" x 3/8", pitch x width. Other machines in the BSA range have sprockets with the same number of teeth, but use a narrower chain, which is a bit puny for the high power output of a well sorted A.
So, the answer is that a 19 tooth sprocket 67 3065 plus gearbox sprocket seal 67 3067 is what you need. The seal retaining ring is the same for all boxes, 67 3026, if you need a new one.
Swarfy.
