While you can already watch your favorite British TV programs on your iPhone using the BBC iPlayer service from their website, it looks like the BBC are developing an iPhone App which should bring a wider range of new BBC iPlayer services to the iPhone.
The new BBC iPlayer app even could feature a download option, which would allow you to download your favorite TV show directly to your iPhone. That way you could watch it whenever you want. Some other features include the ability to watch live TV. There’s nothing official from the BBC yet on when the app will be available.