Concentrate on looking for lunch on Xmas Day. Virtually nowhere will be open in the evening (excluding "ethnics")
Prepare to be spending significant sums of money. For example, my local pub is charging £89 for Xmas Day lunch. And you'll need to make a decision and book very quickly if you want to secure a table.
Unfortunately for visitors, Christmas Day and the 26th (Box Day) aren't at all like what we are used to in the States. There is little public transportation here in London and many places are closed, and the ones that are open charge through the nose.
If you can't find a pub, I'd suggest going to Chinatown or to a hotel (very expensive for the latter). There was a similar question here not long ago with some good replies so you can use the search engine and maybe come up with that.