BBC iPlayer at last works on the Nexus 7, I don't know what took the BBC so long anyway.
BBC has released the "BBC Media Player" app which now enables devices without Adobe Flash to play content from BBC iPlayer.
When I use the app and want to go to BBC iPlayer it seems to direct me to the Chrome browser and opens up the mobile version of BBC iPlayer. You can play the content but it seems to be a very awkward process which isn't very smooth.
You'd think with the BBC being one of the best, if not, the best TV broadcasting company in the world that they could at least bring out a basic app to play video content. Who knows what they're doing.
But to get the iPlayer on Android Jellybean devices you'll need to download and use this app.