If you have internet (and you’re reading this, so, you do) then you can listen to BBC radio live for free.
I’m sure you won’t like everything they play, but there’s bound to be a station you do like (generally Radio 1 >> for teenagers, Radio 2 >> for people too old to listen to Radio 1 any more, Radio 3 >> classical, and Radio 6 >> for people who just like music). They do have playlists, but money doesn’t come into it.
Oh, did I mention that because it’s the beeb, there’s no adverts?
If none of those take your fancy, there’s TripleJ, an Australian station (again with no adverts), who play a lot of of Aussie music which you won’t have heard before. Not sure what their daytime stuff is like, but the evening shows are good.