Hire our own car or do a group tour for weekend trip outside of London?

We're going to be in London for a week. Have been many times but never explored some of the further sites that are a day drive away -- Stonehenge, Bath, Stratford, Oxford, etc. So thinking of using the weekend to do that.

Which would be better -- finding and booking one of the group tours that do one long day or 1 overnight or hiring our own car to drive ourselves for the weekend?

We are from the US, so used to driving on the other side of the road and have never driven in England. However, I have extensively driven rentals in Australia and New Zealand so got used to it. Wouldn't want to drive urban London more than necessary, but could rent somewhere near the edge of the city -- like taking the train to the airport first or something.

Any thoughts on the itinerary are welcome too. We want to see some of the most famous stuff outside of the city. Are not foodies so don't care about that. But do like very nice accommodations if we stay the night somewhere.