As a lot of the previous answers have said, a summery wedding type outfit would be ideal, a hat is a must, you'll be in the minority if you don't have one, shoes - definately go for low ones, or you'll be like some of the women I saw, either sinking into the lawns or trying to smile while obviously suffering from horrendous blisters!
By the way, have something to eat before you go, the sandwiches and cakes etc are lovely but served in miniature portions, and unless you don't mind looking greedy and piling your plate up you'll be starving by the end of the day!