DO NOT stumble off a plane and into a car, all jet-lagged and disoriented! We once spent a few days in/around London and then rented a car for a drive up around Scotland. That was doable- just. Seemed like every morning we would start out and my wife would have to say, 'Ahem, you're on the wrong side of the road!'

Europeans have much better public transportation than we do. London city limits car traffic pretty tightly and you just don't need the headache of traffic and parking. For jaunts further afield, take the tube out to Heathrow and rent from there.