Don't forget the London Congestion Charge zone
You have to pay a small fee to drive into central London—which I don't recommned anyway.
Since you have absolutely no need for a car in London (indeed, it would be folly to try), just arrange to pick up or drop off your rental vehicle at an office outside the congestion zone. Problem solved.
For the record, the town of Durham, England also has a congestion charge zone (in fact, it was the first).
Manchester has debated one, but seems far from willing to enact it any time soon.