Well, this is embarassing
I very much hope that I haven't wasted anyone's time, and I have learned a lesson - never post up for help without having seen the frame first.
The lady I bought it from assured me it had the HH code on the frame. It turns out this isn't true at all. The frame is marked with the number 8242. Unless anyone has any other ideas, I'm going to assume it was built by Ted Pritchard in Chobham.
It also has the name of the owner painted on, and their bicycle club - Camberley Wheelers. The club merged with the local Farnborough club in the late '60s. I guess this pretty much all adds up to this being a nice enough lightweight frame handbuilt in Surrey in the 1960's?
Pics attached, and sorry again for posting before possessing the frame. Sorry folks.
If anyone is still talking to me, I would appreciate suggestions for what to build it up with. I do want to ride it, so maybe all period correct isn't practical for a bit of (mild) touring. I have a Shimano Arabesque groupset ready and waiting and a nice Wrights saddle...