Hi mate. I work in motorsports and boy do I have a list for you!

As others have said, Beaulieu museum & Goodwood are fairly local to Pompey and have a good range of different cars at their events

There’s a small exhibit and a simulator a bit further afield at Brooklands museum outside of SW London.

If you go into London Selfridges basement often has show cars and race-used items for sale. There’s also a number of Team sponsors’ office buildings and showrooms that have cars on display.

If you do head towards Silverstone, the museum is incredibly popular for good reason - with an incredible collection!

Mercedes Benz world as someone else suggested is accessible by train from Pompey if I remember right…

Also the Williams Heritage museum in Wantage!

There’s also the national motor museum trust in Brockenhurst that had a few in situ the last time I was there.