From Christmas Eve afternoon until the 26th December almost everything shuts. Exceptions are restaurants, pubs, corner shops and (some) fast food
There are no buses, trams, trains or even the London tube running on Christmas Day. So your only option will be taxis or maybe an Uber if they are where you're located.
Restaurants will get booked up in advance, even if you're staying out of the cities. Make sure you've booked your meal if you want one!
Most locals will spend Christmas Day at home but many will choose to get some fresh air at some point in the day. It's a great way to connect - everyone is happy and wishes each other a good Christmas!