First ones I thought of was The Ruttles and then many years later Oasis.

funny british christmas song
http://m.youtube.com/watch?v=LmN5ueKucMg

If you want Christmas parodies, Bob Rivers is the undoubtable king.
He's done 5 albums full of it. Start with 'Twisted Christmas'

Thanks

The Destiny's child Emotions one! Brilliant

I remember the Star Chicken song.