I would imagine at least 8ft height wise. I think ours is just under 8ft and apparently the lady before us travelled her 17.2hh in it - although personally I think it would have been lacking head room!
The Bateson Deauville that I have is 7ft and is supposed to take up to 17.2hh. The tallest horse I've had in it is a 16.3hh hunter and he had plenty of clearance (a good foot) but i suppose it depends on how high the horse carries his head.
depends on how high your horses head carriage is. My lorry head 8ft headroom, but it was a struggle to find something that big. 7ft I would say is no where near big enough though. Am having a new lorry built at the mo with 7ft 10 headroom which is fine for my 17.2