For general moving files/folders then it is worth getting a file manager app, it seems Android doesn't include one as standard. I recommend ES File Explorer, its free. Then its easy to cut/copy/paste/move files and folders.
Though yes, the problem is many apps will only look for files in a specific place. You might be able to change that in the settings for that app, though as above it seems its not possible for Iplayer.
You could create a "symbolic link" so the folder in the internal memory points to the memory card. Though that would probably require root.
Or you could use get_iplayer to download programmes from Iplayer on your PC. Then copy them onto the tablet, and play it using some other video player.