This should be the simplest of fixes. You need the correct seal, correct spacer and the correct drive sleeve. The problem with all old bikes is whether these bits are as they should be or a previous owner's failed attempt.
The seal should not be a problem, plenty available online. I do not think it is a widely available "Industrial Standard" offering, rather a BSA special, so an exact match to original may not be available from your local bearing supplier. I'd try Priory Mags, as suggested.
As with bearings, the dimensions of shaft, housing and width define the size, followed by the type of seal lips. Fit with the spring facing into the crankcase, it just pushes in onto the bearing outer race. Factory usually gave the case a few punch indents to make sure it stayed in place.
Fit the spacer with that relief chamfer facing towards the crankcase. This means the spacer does not bear on the relieved change of diameter in the crank at the bearing position. That's wot bergs said (see previous post) while I was typing this.
I've always fitted the seal, then the spacer. Anyone any thoughts on fitting seal and spacer together.?......I wonder if the spring always stays in place doing it my way.
Swarfy.