I took 3/4 of this trip in 2019. We visited London for 4 nights, picked up a car at Heathrow, traveled to the Cotswolds for 4 nights, then went to Cornwall for 4 nights, then drove back to Heathrow. Cotswolds to Cornwall was the longest drive. We stayed in the Northern Cotswolds (Snowshill) and it was slow getting to the main multi lane high ways.
Cornwall is a bit of a haul to get there and only worth it if you can spend more than 2 nights. (IMHO). You don't say what you are planning on doing for this trip. We allowed time to do an all day walk in the Cotswold, and an all day walk in Cornwall. We had 17 nights, and it would not have worked to fit Wales in too.
Picking up a car at Heathrow is easy. You are on a freeway from the get go. I think it is a better option than Oxford where you will immediately be driving on smaller roads through smaller towns. My husband appreciated having time to adjust to the car and re-adjust to shifting with right hand while driving on the left side of the road for a couple of hours before tackling towns.
You have received some good advice about laying out the trip. I would just add that if you do drop the car in Wales, there will probably be a drop off fee. We picked up a car in Wales and dropped it at Heathrow in 2002 and had to pay one. (I don't have the paper work anymore) In 2014, we paid $50 to pick up at Heathrow and drop off in Scotland. For us, it was worth it because it allowed an additional full day in Edinburgh that we would have had to spend driving back to Heathrow.