As the only one who I think has recently mentioned Byford (that's them I'm wearing in my current avatar), I can tell you everything I know, but not if they are available in the UK.
They're probably my favourite undies currently.
They are marketed as 'Byford of London' everywhere I have seen them in Asia, but I have not seen them in the UK (well London really, since that's the only place I've been semi-regularly).
I have a vague memory of someone saying that Byford has a UK 'history', but then sold the name to an Asian outfit. I think Byford's head office is now in Hong Kong.
The sale story may or may not be true, as many Asian fashion manufacturers (including undies) pretend to have European origins (generally British, French, or Italian) by giving their lines anglo/euro names. I suspect it allows them to charge a premium for the perceived quality.
I first found Byford in Singapore, where they are in all the major department stores. I recently found them in large numbers in Kuala Lumpur. They now have a large range, from classic white briefs to trunks and bikini briefs. They're quite cheap, esp given the high quality - less than US$10 for two briefs or one pair of trunks.
The web site does list some US outlets, but I wonder if they only carry their socks or other non-underwear ranges (perhaps someone in the US can check) ? If they are 'coming soon' to the UK, it may be the same there.
The sizes I've seen are always 'Asian' in scale. eg XL is about a 34. I have both L and XL, which by the time I blow dry them are around 31-33. As you can see in my avatar (and gallery), they're roughly a mid-rise brief. The butt is not overly 'generous', consistent with the tight little Asian variant.
They're very soft and quite stretchy, which is why they are so comfortable. They have traditionally had a classic look, with a single blue stripe. The newer range I have seen in KL and Thailand has a wider range of dark solid colour briefs, and stripes on the white briefs. I picked up a box with one pair with a red stripe, and one with a green stripe.
I can't recall seeing them last time I was in Hong Kong, but I'm sure they were there. They are also in some of the upmarket department stores in Bangkok, but about 50% more expensive than Singapore or Malaysia.