Try contacting Sustrans for a list of the cycleways. There's not as many as on the continent, and they're not as good, but they're better than the roads.
As others have said, Cornwall is great, and the lake district. I'd miss out the North West, which is where I have the misfortune to live, and probably the midlands. But I'd definately go for Suffolk, which is how England used to be, and Norfolk, which is big and flat and a bit mad, and North Yorkshire/Cumbria, which is just wild and wuthering. Then I'd get the hell onto the continent and see how much better they do cycling in the real world.
Call me jaded, but I'm just back from 3 weeks in Austria/Bavaria...where it's all just so much better.