I went to Duxford last month. We took a bus to the middle of nowhere and was told that there was a separate bus which continued to the museum. After waiting for about 45 minutes for that one to come and figured it was never going to come, we decided to walk the few miles to get there. Luckily, there is a walkway to get there.. Taxi would be the best way if you didn't have a rental car.. It's a flat fee to Duxford from Cambridge - I can't remember if it was GBP20 or 30 one way. The staff at the shop are very helpful so you can get them to call a taxi when you're done. Otherwise there's a sightseeing hop on hop off bus for Cambridge during the summer and that makes its way out to Duxford. GBP16 by memory but we decided to go for the public transport option which failed!
It's such a good museum - it has gems such as the
SR-71 Blackbird, Concorde, B52, VC10, Viscount, Trident,
U2, Ju-52, Comet, Handley Page Herald.. The list goes on and on. I haven't been to Brooklands but I can definitely recommend Duxford.
It's all about the destination AND the journey.