In reply to:

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Are there any local stations in the UK?

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Yes - mostly single transmitters, AFAIK. There are regional BBC stations, typically covering one county or large city. Independent local radio stations cover a similar area, but they are more common in large cities, and often don't cover rural areas. RDS can link networks of local stations together using EON in a similar way to AF linking different transmitters of one station.

And there are community radio stations, often with a short-term licence (e.g. one or two months during the summer) and student radio with very low power transmitters covering a university campus.