A bit of an update.
I reached for the cheap guestimator again and got these measurements:
Inner Diameter of the bottom headset race that goes on the forks = 26.30mm
That is a Richey Logic I just found in the loft.
Diameter of the metal it is supposed to go on = 26.80mm
The guestimator is probably not 100% accurate; it is a Clarke after all! I have measured a few times though. Half a poxy mm! That is only 0.25mm per side.
I have checked the threads and they seem to match. I just need to make it fit. I think I am going to file/sand the headset piece until it interference fits the forks. Before I do that, I'm going to make sure the other bits fit in the frame.