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.
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
When you click on links to various merchants on this site and make a purchase, this can result in this site earning a commission. Affiliate programs and affiliations include, but are not limited to, the eBay Partner Network.