A series of BBC radio shows to mark the Stones anniversary can now be listened to again for the next few days :

http://www.bbc.co.uk/programmes/p010vkpz

This one, 'The Rolling Stones at the BBC' is especially good - http://www.bbc.co.uk/programmes/b01ntl2t

And not forgetting that tomorrow is Rolling Stones night on BBC2 with the showing of Crossfire Hurricane, Rock n'n' Roll Circus and "..sings the Rolling Stones" (a compilation of other artists covering Stones songs)

Part 2 of the BBC's Stones fest is next Saturday (24th)

BBC2 :

21.45 - 22.45  Crossfire Hurricane (Part 2)
22.45 - 23.30 The Rolling Stones At The BBC
23.30 - 00.30 The Culture Show (Keith Richards interview from 2010)

(followed by 'Dawn of The Dead' - just a coincidence, of course...)

and on BBC4 :

23.30 - 01.10  Muddy Waters & The Rolling Stones - Live At The Checkerboard Lounge