Get flash from here: http://download.macromedia.com/pub/flashplayer/installers/archive/android/22.214.171.124/install_flash_player_ics.apk (think that's the most up-to-date version)
Get Firefox beta from the play store
Force desktop version of the iplayer site when you visit it, and all should be gravy.
Alternatively, wait for the BBC to sort out their damn app so that it works properly on larger android tablets (been through this with my Nexus 10, less than impressed).
Think I'll just switch everything off.