Are you planning to have a car in Central London? That will be quite the experience. I have to drive into London, Oxford and Cambridge quite often and none of those is an experience to be anticipated excitedly.
London: there is the expensive Congestion Charge which needs to be paid online daily, the very expensive ULEZ (Ultra Low Emissions Zone) charge which must be paid online daily. Parking is extremely expensive. Most street parking is restricted, or short term only and very expensive. Garages will run £10 to £20 per hour. Figure £50+ for a day if you don't move the car. Valet parking is only at the very top hotels, if even there, but I suppose if you are staying there the cost is irrelevant to you. Much of London has adopted 20 mph camera controlled speed limits (more cameras per square foot than anywhere else) but in Central London that's a bit of a joke because it is often faster to walk. Remember bus lanes (camera controlled), Box Junctions (camera controlled) and cycle lanes.
Oxford: the city council is actively discouraging use of the motor car, with some concessions for EVs. Driving is a nightmare because of these policies, with frequent barriers prohibiting through traffic, and one-way mazes. Street parking is mostly restricted and where there are a few paid spaces competition is very high so you will often go around and around waiting for an expensive space. Use the Park & Ride lots out of town. Bicycles everywhere.
Cambridge: Traffic is heavy and slow. There are several carparks in the centre but they have high price-tags. I think there are bicycles than in Oxford, if that is possible. Use the several Park & Rides. A car is convenient for Duxford and the Cambridge American Cemetery and Memorial.
But the best advice, unless you have special circumstances, is to forget the car and take the train. Oxford, London and Cambridge are all extremely easy by train.
