It has always been extremely difficult to get the BBC (or for that matter, any of the TV stations) to identify incidental (i.e. background) music used in programmes. This has always been the case. There are however some heroic exceptions; for example I received for Christmas a few years ago the complete A-Z of Dad's Army which listed every single scrap of incidental music used in every episode (even if you only heard a few bars!).
Part of the reason for this is practical, and part (possibly) legal. The identity of background music may only appear on "running order sheets" used solely by studio or continuity staff, which might not be kept after the programme is over. Also, these days, the BBC/ITV etc. do not themselves make the programme; it might be done by an independent production company (I've tried following this trail before, and given up in frustration).
The legal bit might be because the music has not been commercially recorded, but recorded specifically for use in other media (e.g. film, television) and where different copyright provisions apply.