Heathrow is on the western side of London so you wouldn’t have to deal with central London traffic if you rented from there. You could get the heathrow express from paddington station out to the airport and then rent a car from there.
The other option I would maybe look into would be getting the train from London out to Bristol and renting a car from Bristol airport. It’s been a long time since I was there but I remember it being easy enough to drive from there and it’s close to Bath.
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