I have rented a car in the UK twice, once for 4 days and once for four weeks.
We have driven all over England and South Wales and loved it.
Here are some tips.
1) Rent a car with an automatic transmission, if you rent a manual, you will have to shift with your left hand and it will distract you from focusing on driving.
2) Rent a large enough car to have a trunk (boot) large enough for all your luggage. Leaving luggage and valuables in view in your car can lead to someone breaking into your car.
3) I prefer renting from US car rental companies, since I had a bad experience with Europcar.
4) While driving, concentrate on the road and my wife would help, reminding me to "stay on the left." When turning at an intersection, that is when you are more likely to make a mistake, so focus on staying on the left.
5) Don't speed, I tried to do that, but still got a ticket for 40 GBP for going 35 MPH in a 30 MPH zone.
6) On our last trip of four weeks, we didn't do London, but loved the countryside. I planned every day's travel in advance. Of the 28days we only drove more than 2 hours three times.
When driving in England, stay as far away from big cities like London, Manchester and Birmingham as possible. It is ok to pick your car up at Heathrow, but don't recommend driving far the first day after flying into the country. You could rent from Oxford if you are visiting the Cotswolds, Stratford Upon Avon, Stonehenge and Bath.
For Bath, I recommend the Brooks Guesthouse and the Scallop Shell Restaurant (best fish and chips in England).
For Chipping Campden, recommend the Volunteer Inn. They have the best pub in town and a great Indian restaurant. Also, rooms are nice and spacious. We used Chipping Camden as a base to visit Oxford, Blenheim Palace, Stratford Upon Avon and the Cotswolds.