I concur with the suggestion to visit the National Motoring Museum at Beaulieu (unbelievably pronounced Bewley). Last visit was many years ago so see their website to confirm, but they had the most astounding collection of land speed record cars. There’s nothing like standing next to the Seagrave aero-engine to get the scale. I believe the grounds and house were the personal property of Lord Montagu who liked collecting cars.
Also I really enjoyed skipping the rental car. I got to interact with the locals in the tubes, bought a “tea, white” (with milk) at a railway station and was addressed as “Love”, rode a rural bus decorated by the factory to look like an American land yacht with swooping chrome spears (and also a double decker bus and a black cab in London), and at Beaulieu itself, an electric tram pulled by a cable across a little viaduct to cross a pond. It looked to date from Thomas Edison days and I hope it’s still there.
Finally, buy a bunch of Kit Kat candy bars. They look the same as here but HA! They’re completely superior, much crispier, and a quality of chocolate that will spoil you forever.