I went this year and this experience was insane. You see more passionate racing fans in Europe.
I stayed in London for the first half of the trip then moved to Northampton by Thursday. Take the train from London Euston to Northampton and you are all set. They sold shuttle buses for 45 pounds good for all 3 days and the buses were great unlike COTA lol, but obviously expect traffic post-race, but it's nothing horrible.
I would buy an F1 Experiences package so you can get a pitlane walk and the F1 Live event, and the badge will grant you inner track access as well so you can go to the entrance of the paddock and support paddock. I got to meet a lot of F2/F3/W Series drivers that way. Merch prices were also very fair over there unlike COTA. Best thing about this race is getting to see relevant feeders to the F1 ladder and not the damn Porsche cup with 50 year old drivers.
If you fly in the day after just make sure to book a night stay near Heathrow so you don't miss your flight.