If your engine continues to run with the ignition switched off, then your switch isn't wired correctly. But this would happen every time... So I guess you can rule this out.
If its not actually running, but just being turned over by the starter, then I'd say solenoid. This could be intermittent. Current replacement parts are generally garbage and their life expectancy is maybe 3 years. You might have gotten a particularly bad one.. -Britpart by any chance?
The starter could be sticking in the engaged position, but why would it continue to crank with no power going to it? (Ign. switched off)
keep us filled in!
~Steve
---- 1969 Bugeye ----
---- 1962 Dormobile ----