Hi Jim,
I have not cut British threads on my lathe but a Sherline can cut all of the thread counts you listed. The trick is to get the pitch right, as you well know, and the Sherline can cut most metric pitches. British threads often have a more radiused profile so you will need a more rounded tip radius on your cutter but they use a 60-degree included angle so rounding your standard cutter will work.
I suggest calling Sherline to see if their screw-cutting attachment will accomodate your needs. Threads are cut manually on a Sherline lathe but I can attest that it works really well.
Mikey