Radio stations have to get their money from somewhere. (Radio 2, for example, has to pay around £100 in broadcasting rights for every track played on air). So the
only non-commercial stations will be either those owned by the BBC or small community radio stations.
The output of community radio stations varies widely, to reflect the needs of their local communities and, as they only each serve one town (or similar small area), it's impossible to point you towards one for your part of the country without knowing which town (or local area) you live in.
BBC local radio stations tend to broadcast a lot of speech content, even within their music-based programmes, simply because they can't afford to fill all of their broadcasting time with music. I've worked as a relief presenter for BBC local radio and you have to learn how to waffle if you're only allowed to play ten (or sometimes as few as 6) three-minute tracks in an hour-long programme!
So you're not going to find exactly what you want via any stations broadcast over the airwaves. However you might well find something to your tastes on the internet. I suggest taking a look to see what's available online via your computer and then, if you realise that you can get what you want online, buying a proper internet radio (which takes its signal from your router).
This is a good place to start looking for internet radio stations:
http://tunein.com/radio/Music-g1/
(Click on your preferred genre).
Some stations will have loads of advertising but others will have hardly any (or be totally advert-free).
This is another useful index of online stations:
http://www.ipodder.org/radio