It depends whether you are going to rent a car. You do not need a car in London and can probably do London in 3 days. You can do Cotswolds in one day if you hve a car (I think you need a car if you would like to see the little towns in Cotswolds). But you are using train to go everywhere, you will need more time for transportation. We did England and Scottland in 7 days but we had a car.
We did England and Scottland in 7 days
but we had a car.