Back when I was single I would hop on a flight to London nearly every Christmas to see a football game or the lights on Oxford Street. The prices weren't that bad vs. normal prices, but there were some downsides:
a) Christmas parties made hotels in London hard to find (and taxis even worse).
b) The country shuts down for Christmas and Boxing Day. Sure you can get a curry or some Chinese here or there, but there is no public transit, no rail service, and very little else to do on the actual holidays.
c) It's quite cold. A damp wet cold. It may say it's only '40f' but it feels like 20f.
d) It gets dark at 4:00pm, which can be a tad confusing to your jet lag.
That said, there is still plenty to do. There are a few Christmas markets set up in London and other cities, and there are several kid-friendly shows to see in the West End, or even a more traditional Christmas Panto. Nearly every football team has at least one if not two home games between Christmas and New Years so its easier to get to a match. The lights on Oxford, Regent and Bond street put the US to shame. Ice Skating rinks around town, huge post-Christmas sales.