Oxford Would be a great addition to the list - From the Cotswolds by car it is roughly a 45 min journey we stayed at the Cotswolds and visited Oxford for the day and from London by train it is roughly 80 min give or take.
In Oxford you can explore all the historic buildings of the oldest university in the English-speaking world, it has evidence of teaching as early as 1096, making it the second-oldest university in continuous operation globally and of course if you like harry potter you can visit where they was filmed.
Also near Oxford and the Cotswolds is Blenheim Palace the birth place of Sir Winston Churchill. If you go to Oxford there are also many walking tours you can take and i highly recommend doing that if you have a short time, it is a sure quick way to get a lot of information and visit the main locations in a short time. Believe it or not not one of the buildings / colleges have names outside and you will have no idea what they are or what you are looking at.
A tour we took when i visited recently was Oxford magic walking tours we all had a great time if you go check them out the guide was great https://oxfordmagictours.com/ The tours was very reasonable priced as well we did see other tours charging double and we visited all the same places. If you wish to visit Blenheim Palace they do recommend booking tickets in advance learn more about the palace on their official website. https://www.blenheimpalace.com/visitus/
I do hope this helps - Enjoy your time in England