I am not sure if this is common knowledge or not (I only discovered it recently).
The Wii has a built in wi fi connection. If you have a wireless router you can connect your Wii to the wireless router and then to the internet.
One of the options on the Wii will become the BBC iPlayer.
You can then use your Wii to watch the BBC iPlayer on your TV.
You can "catch up" programs you may have missed and so on.