Denham is a good bet. I did my PPL there without a car and didn't find it a problem. Trains leave from Marlybone every half hour to 45 mins. Takes 30 mins to Denham station then a 15 min walk to the airfield.
I'm planning on training for my CPL at Stapleford which again is commutable but I think it takes a bit longer to get there as the tube and bus has to be used!!