I would think for a specific single, the music goes to the record company that issued that single, in order for the writer and performer to get their fee.
I think payments to the Performing Rights Society are blanket payments, and are distributed to the music companies as far as I am aware.
I believe the PRS actually do the distribution, at least that's what I'm led to believe. I'm just interested to know how much the Beeb has to pay for each single. There's a sliding scale, depending on the potential audience, so somebody broadcasting nationally will pay very much more than somebody from the Outer Hebrides Broadcasting Corporation
For most broadcasters, the PRS licence fee is paid as a percentage of their advertising revenue, with larger stations paying a larger percentage. For the BBC, which has no advertising revenue, it's based on audience reach, so a BBC local radio station pays less than a national station like Radio 1.