Hmm, just call me cynical, but I wonder if your house really does flood or whether you just added that later because you weren't getting the right sort of answers to your original question about your garden?
If both your house and garden flood, I wonder why you'd only mention the garden to start with? I would have assumed your first question would be concerning a spring in your garden which floods your house.
As has already been asked, and which you didn't answer, if you owned the house what would you do? As your garden is so large I'd assume it could easily accommodate a pond or two? Or turn the wet areas into a wetland garden with paths, small bridges, reed beds etc. How about building raised wooden playhouses for the kids, which obviously sit above ground - children love them. Of course, with these ideas, you'll have to do some work yourself instead of looking to get the council to do something with your garden.