Well, Ken, those last few photos really do seal your frame's fate. It is definitely a Hill Special. In addition to the scalloped Chater ends, the spear-point top-eyes, the Mk1 Nervex lugs, the frame has the signature Hill Special rear brake bridge with its wrap-around prongs.
No shadow of a doubt at all its a Hill Special.
Have a close look underneath the bottom bracket shell at the edge of the shell on the L/h ie non-chainwheel side. Hill always stamped the frame number in very small characters at that point.
I have checked with a lady's Hill Special Mixte frame today - one a rare breed. The frame number is just at that point on the shell...but very faint indeed. If the frame has been repainted, and sand blasted a couple of times the number could have been worn away somewhat. The Mixte is E417.. making it 1952 or should that be 1953...and the number is stamped very neatly on the fork column. As I said yesterday, I think that your frame's fork is not original as both the Wagner fork crown and the large size of the characters is wrong
I've just taken a five-minute breather to check out another site - http://www.classiclightweightcycles.co.uk run by Peter Underwood and his wife. Robin Hatharall, of Clitheroe, Lancs, the VCC marque enthusiast for Hill specials, has written a full history of the brand. He also displays various photos of bikes and catalogues. If you check on that page you will find your frame listed.
It is called the Road Path model..and Hill calls the lugs by the same name in his catalogue, The unique brake bridge is also illustrated. Hill used a lot of Nervex lugs including the Serie Legere ones, particularly in the early 50s when they became readily available
Your model frame is shown with the matching Nervex Pro fork crown ie the one with the two little prongs that continued to be used with the more famous Nervex Pro Mk11 lug set.
So there you go...Get in touch with Robin. He gets really excited with each new discovery of a Hill Special frame..and, checking his list, he has not recorded my Hill Special Lady Mixte yet
Norris Lockley
Settle UK...just about sixteen miles from Padiham and Adam Hill's former workshops.