I'd say be clear on what you want the bike to be for. A clunker tribute? or something that can go over the hills in Dorset? or a recreation of a UK 70s bike? Any touring?
Reading between the lines, it looks like a 1980s lugged, steel frame with a level top tube, rack mounts, riser bars (or cow horns if you remember flares) is in order.
Lure the beast with a wildcard search on the bay: (tange,531,501,4130,Cromo,cro-mo,cro mo,lugs,Lugged,clunker,retro,vintage,classic,araya,nitto,) mountain
Don't be scared of larger frames. A 1986 Mt Fuji Ltd with twin rollercams would be v. hard to beat.
And low and behold, this puppy is in Dorset:Puppy
K2 is reinforced cromo so excellent for tyour needs. Strip off the tat, sell the flex stem and deck her out with old suntour and a B72 saddle and you're in business