I stayed in Winchcombe last fall. No train service so I'm curious where exactly you are training to in the Cotswolds and how you are getting to Winchcombe.
I flew the red eye from LAX to LHR and got my rental there. It was a stick but that was fine. I'm of the generation that learned to drive with a clutch. Unfortunately the previous renter had done damage and once I got to Winchcombe ( 2 hour drive on major highway and small roads) I had to call Hertz and arrange to for another car. Next morning followed the very pleasant repair truck driver to Cheltenham and dropped off the car. Climbed into his truck and was driven to a very tiny rental car office somewhere. Honestly, no clue where it was located except somewhere between Cheltenham and Winchcombe. Place was so small had to wait an hour for another rental as one had to be returned, gassed up, washed and cleaned.
Not the most pleasant way to begin my Cotswold visit but staying in Winchcombe was a blessing. It was quiet and nary another tourist to be seen. Unlike Bourton on the Water where, even in late November, hordes jammed the walk way and paths.
Great Airbnb stay. 3 pubs, to rest weary feet after long days of hiking and I could walk from the AirBnB to Sudley Castle for the stellar Christmas light show. Great bakery, nice shops in Winchcombe and the fascinating St.Peter's church complete with cemetary.
Having a car is the smartest way to see the Cotswolds. So yes Heathrow into London and out to Oxford by train OR do what I intend to do next trip. Stay the night at the Premiere Inn out by the car rental agencies at Heathrow. Get the shuttle to Hertz and pick up my rental next morning for my drive towards Wales