Can't recommend anyone on your side of the pond, Mike, but if you wish to retain the flats and proof-marks, it should be possible to 'sleeve' a new barrel into the lopped breech-end of the existing barrel, similar to a sleeved shotgun.

I'd get a second opinion on the relining first, though.

...also, try shooting the rifle with soft jacketed bullets, even if you have to borrow the components: you might be surprised. It may shoot OK even though the bore looks terrible, and it will almost certainly 'improve' (at least visually!) with the passage of a couple of hundred jacketed bullets. Tinker has tested the Hornady 350gr SP for relative softness and pronounced it OK for older barrels like your Henry.