Hampton Court Palace Flower Show - Parking

AMO

Hi all,

We're going to go to the Hampton Court Palace Flower show next weekend.

Not quite sure on the parking side of things.

As far as I can tell, if you're coming from the West you should park at the Green Car Park and if you're coming from the East you should park at the Stud Black Car Park.
(Got this info implied from here:)
http://www.rhs.org.uk/Shows-Events/Hampton-Court-Preview-Evening/2013/Getting-to-the-Exclusive-Preview-Evening

Also, it states that parking can be booked in advance:
http://www.rhs.org.uk/Shows-Events/RHS-Hampton-Court-Palace-Flower-Show/2013/All-Coverage/Articles/Plan-your-visit/Travel
When we booked our tickets we weren't asked about this and just stumbled across this recently.

How important is it to book a parking space in advance for this show. Is it a large open field or is there fixed limited numbers of parking spaces?

As it's only a week away, I don't want to call and book to find that they will take a long time sending out the car park ticket (our entry tickets took a while to come through).

Thanks