TWA no longer exists (in the UK anyway) - promoter Scott Conway has emigrated to Thailand, where he has set up shop as a wrestling promoter over there. So that was the end of the TWA and Universal versions.
Robbie Brookside defeated Doug Williams for the All-Star British Heavyweight title at a major show in Liverpool (Robbie's hometown!) in September 2002 and has defended it sporadically since.
WAW keeps its title going but tends to treat it more as a company title rather than a British Title. Premier has always recognised only company titles.
RBW, a New Wave Of Old School type promotion, has stepoped into the Brit Welterweight and Brit Middleweight breaches following the demise of TWA, but AFAIK doesn't have a British Heavyweight title of its own.
NWA Hammerlock recognises a UK title not a British one.
The FWA (despite the hype!) has only just recently re-emerged from several months' hibernation.
So at the moment Robbie Brookside and the All-Star title get the nod. He's not quite undisputed Brit Hwt champ but he's certainly the most predominant one.
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Doug Williams' All Star Peoples' Championship (as mentioned by necrosis) is
nothing whatsoever to do with the British Heavyweight title.
It replaced the World Heavy-Middleweight title. "American Dragon" Brian Danielson won that title last year. That belt was vacant after backstage All-Star commisioner and former champ (undefeated champ since '92) Frank 'Chic' Cullen retired and decided he wanted to have his old title of 11 years carry on after him.
The title was to have been shared between All Star, Stampede and some Puro indies, but after this fell apart, All Star renamed the title the "People's championship", had Dragon job the repackaged title to Williams and announced that henceforth, all Williams' challengers would be nominated by the fans via write-in vote.