How about this: the bike was originally built as a track only frame, and the original (or later) owner decided to retrofit a brake to it. Ergo: "not the cleanest of drillings". I assume that you're aware of the Classic Lightweights UK site,
https://www.classiclightweights.co.uk/. That's where I would be looking for an ID on this. Having thought about that, I imagine that you're going to reveal that you're in the UK, and that's why your first post mentions Carpenter, and discussion with "the registrar" -- more fool me.
Another thing I notice is that the steerer tube seems to be very long for the length of the head tube -- what kind of headset stack would this have? About 50 mm?