We saw the battle proms at Hatfield house a couple of years ago, they were truly magnificent...and very, very wet :(
Whatever you decide to take in terms of food, I'd highly recommend a couple of large brollies and a waterproof. We also took a couple of small, lightweight folding stools which were invaluable as it saved us sitting on the wet grass, the waterproof backed picnic rug was no match for the torrential rain.
It was a great evening though and only slightly dampened by the weather, I'm sure you'll have a wonderful time.