As for Xmas Day dinner, you'd better get on the computer and make some reservations now. You've got a couple of options for finding a table: either go to opentable.com, or go to the Brit version, primetimetables.com. Either will show you what tables are open and at what times. Plus, you'll either get a link to the menu/restaurant, or more info. Be careful to check and be sure that the restaurant you select isn't offering a special, fixed price menu that evening.
You're saying "evening"... traditionally Christmas Dinner is served in the middle of the day, and while things may be different in London out here in the provinces many if not most restaurants are closed in the evening on Christmas Day.