Yes the BBFC is technically a non-governmental body, BUT government legislation gives their verdicts the force of law. Their certification decisions are absolutely binding on videos, DVDs and even certain types of videogames. Retailers can and have been prosecuted for violating the age restricted categories (12, 15 and 18, with an R18 category for hard core pornography requiring a special licence to sell). Cinema releases are somewhat more complicated - basically the BBFC makes a recommendation but final responsibility rests with local government, so the BBFC can be overruled, but that's very very rare. Again, cinema owners can be prosecuted if found to be in violation of age restrictions. To all intents and purposes the BBFC is thus a censorship body.
Needless to say, I also completely disagree with your evaluation of Doctor Who, though I do note that you excluded SOLOists from your description of the show's fans ;-) Sure the show used to be eccentric and at times nerdy beyond belief, but there was always something deeply romantic about this one individual travelling around time and space fighting evil (in direct contravention of a non-interventionist policy adhered to by his people). If anything the revived show is throwing up far more mature and intellectual storylines than was previously the case, to the point that millions general viewers, most of them not nerds or science fiction fans, are now regularly tuning in.