Your travel option for a Christmas arrival is a taxi cab.
Not going to be cheap.
The day after Christmas is Boxing Day.
You’ll need to do your homework to see if specific places that you’d like to visit like the Tower of London will be open.
Day trips: Bletchley Park, Bath, Oxford, Greenwich Rye, Cambridge, Eastbourne, Canterbury.
EDIT: have spent a half dozen Christmases in London. Christmas day is quiet. If near one of the many Royal Parks or the Thames path you’ll find families out and about with new winter coats, hats, coats, bikes, scooters, footballs.
As noted many ethnic restaurants are open for meals but good to make reservations. Some pubs offer dinners. In your Battersea neighborhood. The Lighthouse and the Woodman are good traditional pubs.