While there are lots of data feeds from bbc.co.uk/programmes, described on the developer pages, there isn't yet a) a SPARQL interface to all the data or b) a feed of all episodes. Also the 'is_repeat' flag seems a bit broken, as it only counts repeats on the same channel, I think. This means that it's hard to show "all shows in category x that were first broadcast in the last n days".
I took the approach of storing the broadcast date of episodes locally, allowing this interface (click an image to load the respective programme in the viewing area).
I also put a project in github for the first time, so if you want the code, it's there.