Following on from a tweet on Friday from @gav_richardson I found that you can install an app on the iPhone and stream some of the BBC radio stations. The app you need to grab is FStream. It doesn’t have the best interface but it does work well. Full setup instructions can be found here.
A full list of the BBC radio stations I’ve got to work are:
Unfortunately Five Live doesn’t work which is allegedly due to broadcasting rights of sporting events outside the UK. Another solution is to try the Flycast app which again is free and search for BBC which should return radio station’s 1-4 which you can then select and listen to. At least there is a solution until iPlayer supports radio stations on the iPhone.