You can find out if your BBC local radio station is available on DAB at Get Digital Radio.
If it is not available, it is because BBC local radio services on DAB digital radio are transmitted by commercial broadcasting operators as the BBC's digital multiplex is already used to full capacity for BBC national services. Some BBC local radio stations are not yet available on DAB because they are in areas where a commercial licence has not yet been awarded by the regulator, Ofcom, so there is no commercial operator.
All BBC local radio stations are available locally on FM and throughout the world via the BBC website. For FM frequencies go to the BBC Radio site and look for your local station in the Nations & Local section.