Populated largely by lunching Civil Servants, and the odd Channel 4 bod, the Regency would probably be described as a 'design classic' in an art magazine, or as a 'quintessential greasy spoon' by a food magazine, but it doesn't appear they are that worried about labels.
What they do is good honest British staples, quickly and at very reasonable prices. It's so iconic in its design that it has been chosen to feature in films and TV, memorably in a scene in 2004's Layer Cake. Most notable of all, however, is the friendly lady serving at the tills who can vary her voice from fantastically loud to a sedate chat in the bat of an eyelid. It has to be seen to be believed.
For more, and some fantastic pictures, see here.