I'm from England and I would seriously recommend Derbyshire and Cornwall too. Other than that, you've picked some great places.
For accommodation you will probably find some good deals on Travelodge. https://www.travelodge.co.uk .. Also premier Inn's are a nice place to stay although a little more expensive to a Travelodge depending on where abouts you are.
How do you plan on getting around? Will you be hiring a car? Or public transport?