Can I get BBC iplayer on my Apple TV

No, but I believe you can now air play it from an iOS device to Apple TV.

Jules

There is no App Store for the AppleTV to add things like the BBC iPlayer, so whatever content is on the Apple TV is all you get. If you have a Mac, iPad, iPhone or iPod Touch, you can use Airplay to watch it on AppleTV. I've done this for some sporting events that are only online.