Going to London in January; any side trips worth making at that time of year?

The timing is set on a trip to London after Christmas for about 10-12 days. (This can't change, it's part of a work trip for my husband). We're coming from California, and we know to expect short daylight hours, cold, and rain, so I figure our time in London will be spent in the museums, at shows, and in pubs. Would you recommend any 2-day side trips during this time of year, or would it be better to stay in London? Many, many years ago we went to London during the summer and were able to go to Cambridge and Bath. In January, would it make sense to split our time and spend a couple of nights in York? Somewhere else? Thank you!