ProM
Have you tried contacting Esher College, Thames Ditton. The college is perfectly located to Hampton Court Palce and the grounds, on the Surrey shore line of the river Thames and is within easy walking distance.
If you view "google earth" the college is located just to the south of Hampton Court Rail station. The college has large grounds that could easily accommodate any heli, as long as the college is not open with students during the flower show dates.
ppheli was right - although not an option I should have stated the travelling time from Sandown Park race track is around 10 minutes without traffic/congestion. Especially during a large event such as the Hampton Court flower show.
Give the college a call and see what they say. They may welcome the additional income from landing helicopters?
Secret Service