Actually, finding something open on Xmas Eve is not difficult, as there are plenty of options in Kensington, Mayfair, Soho, Covent Garden areas....depends on your inclination/interest in walking. If it's cold and not raining, it's a great way to finish the evening. 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.