Interesting - the Record link posted by AndyT gives the thread as (non-standard) 7/32" x 20tpi Whitworth form, but as jasonB points out, it would be entirely logical if Stanley used the American thread. However, that's non-standard as well - the nearest UNC size is 12 - 24. As far as I can ascertain, the UNC sizes followed the old American National, previously US Standard. It could be that at the time Stanley were tooling up their factory, the US Standard had not been finalised, hence the use of a thread apparently outside standard.
As the studs for retaining knob and handle screw into fairly short blind holes in the plane body casting, it could be that the use of a coarse thread was decided to reduce the chances of the thread stripping in the iron - cast iron doesn't really like fine threads.
As jasonB says, there is a very slight difference in outside diameter between the American and British threads; there's also a difference in thread angle, with Whitworth at 55 degrees, and American at 60 degrees.
In practice, given the likely fairly loose clearances incorporated at manufacture between male and female threads in both systems for this application, they will in all probability be interchangable.
