My wife and I did a four week drive tour of S. Wales and England (no time in London) in October, 2017.
We visited many of the places that you mentioned. Here was our itinerary with some details:
Bath, we did three nights there and spend one full day exploring Bath and the other on a day trip to Wells and Glastonbury.
We stayed at the Brooks Guesthouse, which is at a great location. Also, the great restaurant, The Scallop Shell is nearby.
We then moved on toward Wales and stoped off at Tintern Abbey and a couple of castles on our way to Cardiff.
Cardiff, we did Cardiff Castle, Caerfully Castle and The Museum of Welsh Life, on our way to Tenby
Tenby, Wales is on the water and historically an interesting city. From there we went to St. Davids, at the SW tip of Wales, a very historic place. On the way we stopped at another castle. Our last stop in Wales was in a small village in Cardiganshire, where my Paternal ancestors came from, leaving to come to America in 1716., then back to England.
Chipping Campden, in the Cotswolds. We stayed six nights and used it as a base for visiting the Cotswolds, Oxford, Blenheim Palace and Stratford Upon Avon. We stayed at the Volunteer Inn, which I recommend. It had modern spacious rooms, good rates and a great pub and Indian restaurant.
Warwick, was next where we spend most of the time at the castle, which is a huge draw for British tourists. We saw many children there. It was good.
York, was one of favorite places on the trip and we did three nights there. Visited a couple of museum that were great, especially the National Railway Museum. We walked the ancient walls and loved the Cathedral (Minster) as well as the narrow streets of the old city.
From York we headed toward the Yorkshire Dales and on the way saw Castle Howard and spent the night (I think it was Pickering) before driving through the Dales all the way to Whitby, on the North Sea (don't miss this place).
Durham, we did two nights there and loved the old city and its historic cathedral. The Venerable Bede's toomb is there.
Then on to Haltwhistle to visit Hadrian's Wall for a day, after than on to Keswick for three nights at The Lake District. We did the drive of the circle around the lake that Rick Steves guide of Britain recommended. Very Scenic.
From there, back down to Winchester for three nights.
Recommend renting a car with automatic transmission and a nav system. Also, make sure all your luggage fits in the trunk (boot).