Im planning to make a trip across UK for 1 week and I would like to visit these places for sure: Cambridge, Stonehenge, Stratford-upon-Avon, Bath, Edinburgh, Lake District, Nottingham.
I do not mind to visit (less desirable than the cities from the first group because visited in the past, but still good options): Liverpool, York, Oxford, Brighton.
I can start the trip from both Leeds or London. I travel by bus (e.g. National Express), what is the best route for me to minimize expenditures (not all cities could be included, but I think 1 city per day is fine and I can travel at night)?