Be sure to plan your itinerary carefully - a lot of attractions are closed Christmas Eve, Christmas, and Boxing Day (day after Christmas). Public Transportation have either limited or no service these days and Taxis charge extra. Also on Christmas, many grocery stores and restaurants are closed. We enjoyed visiting over the holidays, it just requires careful planning. On Christmas Eve we took a guided bus tour of Canterbury and on Christmas went on special walking tours with London Walks.
I was in London the first two weeks of December last year and it was wonderful. We (there was 3 of us) stayed at the Regents Park Marriott and loved it. Very close to the tube and you could be anywhere in no time. The hotel itself has large rooms which is a plus in Europe. We had nice weather, only one day of real rain. Layers are the key! and a good umbrella and your most comfortable walking shoes. As far as things to do - we had most of the toursit stops to ourselves and that was best suprise. We did London Tower on a weekday morning and had the crown jewels to ourselves for almost 20 min. That is unheard of! We did the London Eye and would suggest it to everyone. Buy your tickets before you leave. Also buy your subway tickets before you leave. One of the greatest things we found to do was a walking tour group called LondonWalks.com. check out their web site. You can pick and choose which tours, meet up with the group, pay for the tour and off you go. If you think your going to do more then one tour, ask for the Walk About program. It gets you a discount. We did 3 of them and would have done more, but there wasn't enough time. Another good thing to do is visit St. Martin in the Fields church (it is right on Trafalgar Square). You can get inside, relax and have a good snack or meal and do a brass rubbing for under 5 BPS. This is a great item to take home. We really enjoyed it and got to meet and talk to other people from around the world that were there on holiday. The best part of Christmas in London is that everything is decorated, so get out at night and see the stores and the lights.
My family and I have stayed at several really nice hotels in London. The Lanesborough, Dorchester and Connaught are all fabulous. In the past two years we have taken advantage of Marriott Rewards and stayed at the Marriott Park Lane and the Renaissance Chancery Court. I like both, though the Park Lane is in need of a makeover. It is, however, conveniently located next to the park, Marble Arch tube stop and shopping on Oxford Street. Club lounge is on the first floor. Nice bar and restaurant, though there are better choice for dining nearby. The Chancery Court is my favorite, though. Fabulous rooms, nice lounge and very posh setting. Adjoining rooms are available and the hotel entrance faces a courtyard. There are many, many things to see and do in London, of course. One of our favorites is the Cabinet War Rooms and the Churchill Museum. Have fun.
Regarding accommodations we stayed at a hotel called '196 Bishopsgate' while we were there over the Christmas. Having a full kitchen was an important element of our stay (given many of the restaurants were closed or overly pricey over the holidays). We were pleased with the simple, but modern accommodations.