In general, I think this listed below might be entertaining:
1) Food market -
http://www.timeout.com/london/around...ristmas-market
2) A new flick -http://www.timeout.com/film/reviews/90447/sherlock-holmes-a-game-of-shadows.html
3) Some skating .. maybe ;) -
http://www.somersethouse.org.uk/ice-rink
I doubt it will be COLD, I mean like real cold we get here. -10C + wind

, all the pics of London in December look like it's +5C or even warmer
