I don't live in London, though I work there, and I have to say that there aren't any really unique London Christmas "must-dos" except the things which have already been mentioned, like the temporary ice rinks, the Christmas lights in Oxford and Regent Streets, the usual Christmas shows or pantomimes, many of which can be done in other cities.
London has, though, recently started to have parades on New Year's Day (not really Christmas, though).
If you're meeting your friends on Dec. 18th, the shops will still have their Christmas displays up, but hurry! Some big shops in central London actually take down their Christmas displays before Christmas, to get ready for the sales which often start on Boxing Day.