Slow down, gentlemen. I didn't positively identify it as a Whitworth thread -- it's just a contextual guess because it rang a bell in my hand, but it's a long time since actually worked on a known Whitworth-threaded device. I actually had the bolt and nut on my Brooks out when it came loose entirely by itself, but I didn't put a thread gauge on any part of it because I had only one set of really flat spanners that would fit through the spring, and one of them was a so-so fit, so I bolted the thing up as best I could and was grateful not to have to send it away. It's lasted since. You can't get a thread gauge inside either, not unless you take it apart and even then it will probably be too long to turn vertically for the measurement.
I reckon the factory probably uses an ancient custom tool of their own making, probably in appearance like a larger version of the saddle tension spanner but better made and forge-hardened. Until the war manufacturers had their better apprentices make bench tools*, and the toolmakers who made the prototypes of custom tools were the highest paid workmen.
What would be useful for a Brooks saddle would be a really flat adjustable spanner. (Giving the precision engineers shingles, I know. Sorry, fellows, don't take it out on me, speak to good old Boultby.)
*In Spain, at ENASA, the bus makers, well into the 1950s. ENASA's apprentices actually built the handful of Pegaso, a sports car that left a contemporary Ferrari for dead. l
