If you use your favourite search engine on "Stanley Plane Thread Sizes", there is a wealth of information, all concurring that it's a current non-standard size, some say 3/16"x28, others No.10×28, neither of which help you, because it's no longer a standard, if indeed it ever was one.

Easiest solution to me is to buy an M6 thumbscrew off eBay or similar, and turn off the thread, almost all the way to the top. The remaining bit will allow a nut to be Loctited on and turned down to form a collar.
The rest, when the thread has been turned off, is almost spot on size to cut a 28tpi thread.

(or, as mentioned previously, the thumbscrew on mine is a rattling good fit, so you might just get away with an undersized 1BA @ 28.3tpi)

When you've got those sussed, try Singer sewing Machine threads next, where you will find several 3/16"x28  were used..
https://www.singersewinginfo.co.uk/screw_threads

Bill

Edited By peak4 on 01/12/2021 02:02:11