Public performances of other people’s music must be licensed in order to avoid copyright infringement and also infringement of performance rights (when playing recorded music). Currently there are two separate licensing bodies in the UK who are able to assist: PRS for Music represents the interests of composers, song writers music publishers, whereas PPL deals specifically with recorded music and represents the interests of producers and performers.
It follows that if you are organising a public performance of musical works then you are likely to require both a PRS and a PPL licence (particularly if recorded music is involved). The good news is that it should become simpler to obtain licences for public performance of music. PRS and PPL are working together on a joint venture the aim of which is to offer a single licence. Apparently this is will be ready at some point during 2017.