You can't get digital radio everywhere in the UK yet. Both commercial radio and BBC services currently cover about 90% of the population.
The way that digital radio signals are transmitted (as a multiplex group made up of different stations) makes much more efficient use of the broadcast spectrum, but is still not physically possible for every national, regional and local radio station to be heard everywhere in the UK.
To find out what stations you can get go to www.getdigitalradio.com and enter your postcode.
Can I get DAB overseas?
DAB isn't available in the USA and while much of Europe, Canada and Asia implement the DAB transmission system the frequencies often differ. In the UK, the frequencies used are 'Band III' while in some other countries, the frequencies used are 'L Band'. For more info about DAB worldwide, visit www.worlddab.org