If it were me and I was coming into London for a day trip from the countryside to go to meetings/appointments or just plain ol' goofing around and shopping I would not drive to London unless I absolutely had
to or unless I really enjoyed the headaches driving in London generate. The traffic is atrocious, parking is rare, horrible (and expensive) and you have to pay the congestion charge
to bring a car into central London on the weekdays. Much easier to take the train, tube, cab and walk-especially if all the activities you have planned are in central London or just the West End.
I agree. Didn't think it through -- seems crazy to plan to drive in London.