We took our teenagers to London for Christmas a number of years ago and they still talk about it. My son really enjoyed it but my daughter was a little less enthused about Christmas away from home.
It was cold but it didn't slow us down or keep us inside. St. Martin-in-the-Fields at Trafalgar square had some wonderful concerts and we often ate lunch in the crypt which was always crowded with locals. Decorations are a bit more scarce than in the U.S but we put up a tree and hung some lights in the window of our rented flat.
We also shared some of our traditions with friends in London and our neighbors such as luminarias or firelitos, Christmas sugar cookies and Christmas cards that depicted our home city of Albuquerque. This helped my daughter to feel a little less homesick.
December 25th was a good rest day for us but we also took a guided London walk on December 26th which was really nice as the streets were far less crowded.
Have a great trip!