If you do have problems finding somewhere to eat on Christmas Day, those few pubs that do open for lunch get booked up quickly, it should be easy enough to do it yourself. Traditional Christmas lunches at hotels can be pretty expensive as it is very much a seller's market! Majority of the restaurants that are open will be Asian etc.
Marks and Spencer's Food Halls (much wider choice than their Simply Food outlets) sell the prepared components of a traditional Christmas lunch ie turkey and all the trimmings, prepared fresh vegetables and Christmas pudding. All you have to do is put them in the oven and serve! The food is chilled not frozen and of good quality. Other stores will do the same sort of thing but apart from Waitrose, M&S is my usual choice.
Don't forget to buy a box of Christmas Crackers (not the edible sort!), Christmas cake and mince pies.
Then after lunch join Londoners for an afternoon walk in one of the Parks, then back home for a high tea (if you can face it!) of cold turkey, ham, mixed salad, sherry trifle and cake. After/because of all the eating most of us settle down to watch the Christmas shows on TV/snooze in the evening.
Some pubs will open for a couple of hours midday for drinks only so you could visit one before lunch. It used to be the tradition that the menfolk escaped to the pub while the womenfolk stayed at home preparing the meal and dealing with over excited chidren!
Every year one of the posters on TripAdvisor's London Forum prepares a wide ranging list of info about London at Christmas time. It would be worth your while to print off a copy for reference.