To get around London in a car without getting stuck in a traffic jam in my experience is only possible during the summer months outside holidays with dry weather during the week at night between three and four in the morning. But that should not be the starting point for your journey planning. It is much more comfortable to plan an extra day of travel when going North or West. Seen from the perspective of arrival at Dover, of course. This brings you to the question of where to stay the night.