The nearest train station is Oxford. Trains run regularly to Oxford Station station From London Paddington (53 min journey). You can then take the Bus from Oxford City Centre to Woodstock, Blenheim Palace (38 min journey).
London Heathrow Airport (LHR) is the closest to the festival. From Heathrow Airport London T2,3 take the Bus to Gloucester Green Bus Station (1 hour 10 min journey) and then take the Bus to Woodstock, Blenheim Palace (29 min journey).