You mean
New York Doll? I don't think the BBC was involved in making that (
http://www.onepotatoproductions.com/NewYorkDoll/production.html). Maybe you're referring to another documentary.
New York Doll is a great film (and story) though. Interesting even if you don't give a crap about the New York Dolls as a band, which, understandably, most people don't.
Bob Gruen's
All Dolled Up is great too, though I had to consume it in a few separate sittings. Sound is not always great, it's a bit hard to take for a couple hours straight.
I was excited to see it though, having read in the 70's about Gruen's massive stash of videotape of the Dolls. Never thought it would be released, but there you go.