Wouldn't it fall under the BBC's blanket agreement with the industry that permits them to play any song for free?
Just been doing some reading on the blanket agreement and it appears to be the case that if the BBC has funded more than 10% of the production budget, the production can make use of the BBC’s PRS. So, they can play songs that are on the PRS database. The PRS then pays the royalties to that artist.
It's not free in this case I guess.
So I suppose in a way it's similar to subscribing to Spotify. Paying a fee to a company to get access to a number of songs.