Does this make sense:
1) Taxi Southampton to Oxford (will have lots of luggage, could find no direct trains).
2) Rent car in Oxford (where???). *nervous about the 'other side of the road' driving, avoiding major highways, hence not renting in Southampton.
3) Drive rental car to Cotwolds hotel/villages.
Plan B would be taxi to Moreton-on-Marsh, rent car there.
Thanks for helping with this!