Okay firstly let's ascertain what version of Android your Nexus 7 is running, do you know? Have you updated it?
It'll either be 4.1.1, 4.1.2 or 4.2, to find out go to Settings> About tablet and look at Android version.
If your on 4.1.1 or 4.1.2 you can use the BBC iPlayer app found on Google Play, you'll also need to install the BBC Media Player also available on Google Play. BBC Media Player is a flash stand in but if you've upgraded your Nexus 7 to 4.2 neither of these apps are compatible ATM, I'm sure the Beeb will update them soon though.
They do both work on Android 4.2 but show on Google Play as incompatible, if you install both when on Android 4.1.x and then update your Nexus 7 to 4.2 you will still be able to use both iPlayer and Media Player.