Rihanna performed 'What's My Name?' on the programme, while Aguilera played 'Express' backed by a troupe of scantily-clad dancers. Watch footage of Aguilera's performance by scrolling down and clicking below.
Broadcaster ITV also received more than 1,000 complaints about the programme.
The X Factor winner Matt Cardle yesterday (December 19) went straight to the top of the UK singles charts with 'When We Collide', his version of Biffy Clyro's 'Many Of Horror'.