Centre Parcs is one of my favourite sites. I go every year. They have a wildlife centre with a bird hide.
You should see GSW's, (loads of them!) Treecreeper, most of the tit families, Finches, Siskins, Redpoll to name a few. You'll even see some of my pictures hanging in their display case!
I wouldn't want to walk to Rufford Park from there. It may only be across the road, but the main driveway is a couple of miles long at least. Rufford is again excellent for most of the birds you'll see at Centre Parcs, but not in the numbers. A good selection of tame water birds are on their lake, with the possibility of displaying Great Crested Grebes. I go to Rufford and Sherwood Forest every week, and often two or three times a week.
At Sherwood Forest the best place for birds is the car park. (Hence Rogers comment!) Take some bird food with you and you should soon have a variety of Tits and Finches around you. You can get really close, they're used to me hanging around.
Often the woods themselves are a bit of a disappointment bird wise, although I did last week put some food down on an old rotting post and was soon getting good shots.
You should have a great time there. There's far more than just birds, I never do much more than hang around the nature centre, there's screens with cameras set up on various wildlife.
Good look with the weather!