For the boys, and you, the Tower for sure. Also there's a Harry Potter studio tour or some such, if they're into that. A cruise up or down the river (bundle up). The Cutty Sark at Greenwich and/or Golden Hinde near the Tower. Hampton Court is good, especially the older Tudor part. The Imperial War Museum and/or the Churchill War Rooms. The Eye, on a nice day if possible. The Sherlock Holmes Museum if they like detective stuff. There are fine museums and galleries but maybe not of so much interest to the boys.
Bath and/or Salisbury+Stonehenge would be good day trips. And/or Windsor Castle. But there's enough to see and do in London, and weather may make you want to stay in the city.
Things will be open, daylight limited, dress in layers with something waterproof outside. No turkey unless you go looking for some sort of expat celebration.
Peruse a good guidebook and have the kids look through and find what they'd like to do. Give each person a day or two to call the shots. They'll enjoy it more, and roll with the punches better, if they've been part of the planning.