BBC national and local radio stations are generally available worldwide. However certain programming is blocked to overseas listeners because of rights issues. (In general that means you can't receive most live sports broadcasts).
Simply go the relevant website and click on the 'Listen live' link. The URLs are fairly obvious, e.g. Radio 1 is at
http://www.bbc.co.uk/radio1
You don't need to be a rocket scientist to work out the URLs for the other BBC national stations! If in doubt, just google them, which is usually the best way to find the websites for BBC local stations.
Most BBC radio content is available overseas. I've just connected to iPlayer via a proxy in Bulgaria (so that the BBC server thinks I'm overseas) and I've had no difficulty in listening to stored radio content.
Chris