Some great suggestions so far. Let me add St Albans to the list. Lovely place (technically a city because it has a cathedral) about half an hour out of central London by mainline train from St Pancras. Lovely architecture, very relaxed and some interesting sites such as St Albans Abbey and the Verulamium Roman ruins. Nice market as well, and at Christmas they're usually selling Christmas trees etc, so it has a great atmosphere.
Good point about timing your trip, as things will shut down early on Christmas Eve and stay shut on Christmas Day and Boxing Day. Personally I would aim to be in central London at that time and perhaps do the trip outside London before or after Christmas. We've been in London over Christmas several times and, while shops and transport shut down, it's still a great time.