Right, I've understood my rather basic mistake – my calipers are graduated in decimal parts of an inch, not eighths – so just over 0.3in (i.e. 5/16) rather than 3/8. Lesson learnt.
Anyway, aside from demonstrating my incompetence, and by way of rendering this thread useful for anyone searching in the future, the good people at Colchesterspares.com confirmed that the bolts are 5/16" UNC.
Thanks again to everyone for your patience and advice!