Hmm. The only affordable Nikon zoom which goes to 400mm is the 80-400VR. Whilst it has some virtues, quick autofocus certainly isn't one of them!
Is 300mm enough? The AF-S 70-300mm VR turns in a decent performance for its price, and it's w-a-a-a-y inside your budget.
Or if you can cope with a prime, the AF-S 300mm f/4 is great optically, and around £1000, and will take a 1.4x Teleconverter to get you to 400mm.
Other than that, you're looking for something from the likes of Sigma (eg 120-400mm OS), but I have no experience of them.