The smallest standard Whitworth threads are indeed as you list:
1/16 inch X 60
3/32 X 48
1/8 X 40
So are not arcane specials.
(Source: Bentley, W, Machine Shop Companion, The Bentley Publishing Co., 1913)
That book also gives useful change-wheel tables for cutting inch- and with 127T wheel, mm- pitch threads from a 4tpi lead-screw; which is that of the Harrison L5. Though of course useful to me only if my lathe's wheel set matches the tables!