I have solved one part of the puzzle, the threads underneath are 5/16 UNC. I made an impression of the threads and found the pitch to be approximately 16 to 18 tpi. That definitely narrows it down to BSW or UNC. I had tried what was probably a BSW bolt without it screwing in, but today I had another search of the garage and found a bolt with the nuts on it. The nuts were too small for BSW so it is probably UNC. It is a tight fit, but screws right to the bottom of the hole. Not being able to get to the workshop at the museum because of lockdown is a handicap.
I still will need to strip it down before deciding what to do with it, the rear toolpost for larger boring bars is current favourite, it will be much stiffer than any standard one can be, and 25mm left hand bars will fit it.
I will be asking about this toolpost on the Home Shop Machinist to increase the chances of somebody recognising it.