They weren't allowed to play a song from Elvis that Steve sung, yet they are playing the Scizzor Sisters music? I don't understand now...

My guess is the Elvis performance was cut due to time constraints on the show. Plus it may have been lousy.

Normally the TV companies have a blanket licence with the PRS to play whatever music they like for a fixed contract fee.

Elvis and the Scissor Sisters are different acts, and while one band may happily let a song be played, another estate may not. I remember that they were having trouble clearing some Beatles songs playing in old episodes of 'Doctor Who' being released on DVD.