The venue will almost certainly have a licence for recorded music.

The PRS and other copyright collection societies only have authorisation to collect on behalf of works their members have assigned to them. (The vast majority of commercially recorded music is, so they tend to assume that if music is involved, they need paying.) It would be unlikely that someone who's CC licensed their work will have done so, but checking is a good idea - definitely if it's not one of the 'commercial use ok' ones.