BBC Worldwide. It operates the music licensing, music publishing and international radio operations of the British Broadcasting Corporation. It has primary responsibility for releasing any music original to Doctor Who and its spin-offs. It has been particularly involved in the various Doctor Who concerts supporting the BBC Wales version of the programme, which it co-produced. It therefore also co-produced the televisual recordings of those events and their behind-the-scenes documentaries, such as Music and Monsters.
The phrase "BBC Music" may also be said to be a website — http://www.bbc.co.uk/music — that supports the domestic use of music by the British Broadcasting Corporation, but this is not the sense of the phrase which is most relevant to Doctor Who.