Hello Frances.
I missed this thread when it first appeared.
The spindle threads are 1/2" X 26 TPI and 3/8" X 32 TPI. These threads still exist on the Cowells ME90 lathe spindle.
The collet in your second photograph is a Perris design. There were four standard sizes, according to the brochure, 3/32", 1/8", 3/16" and 1/4".
There should be two threaded holes to the rear of the LH tailstock bearing housing to fit the backgear bracket. From memory they are 10 – 32 UNF, but I would need to confirm that. The tailstock locking bolt could also be this size. It is close to 2 BA, but that does not work properly.
The spindle and tailstock tapers are 0 MT, truncated. Cowells still have them, and are a source of centres that will fit without taking up too much space.
The lathe was available as a number of variants, the plain lathe, which is the model that you own is the basic one. Owners could add backgear and fine feed with the dog clutch to end up with the version seen in the brochure. Screw threads are a complete mix of BA, UNF / UNC, and imperial. Cowells metricated everything virtually as soon as they took over.
You do get the impression that Brian Perris was living from hand to mouth, but the machine that he designed is still in production as the Cowells ME90 machine, forty years later, which says something for his ideas.
If you have any further questions please ask.
Michael Potts.