There are 2 bbc shops i know of. But both are in london.
One is at the BBC Experience, at broadcasting house and the other is only avalable to people who visit tv center. theres info on tv center tours/ audiences on the bbc web site.
(i went on a tour of the bbc last year but they didnt have any news stuff unlike NBC who have loads of news stuff Even NNBC News cuflinks.....How usefull....)
I'm near Manchester, but to my knowledge their Oxford Road studios don't sell stuff.
Granada did, of course, have their own studios tour ( well, sort of - you didn't get IN the studios ) and sold their own merchandise - but alas - now closed.
Otherwise BBC Broadcasting House, London I think.