For driving anywhere in Europe, the first thing you'll need is a decent route planner. This is by far the best one:
http://www.viamichelin.co.uk/
(Note that you can choose 'sightseeing' among the options).
While the UK has some fantastic places to visit, I can't really see the point of spending more time on this side of the channel than you need to (e.g. by driving up to Scotland). Save that for another trip.
Further, I'd advise against trying to cover too many miles. If you want to really enjoy the trip, you probably don't want to spend a high percentage of your time driving.
Harwich is an easy drive from London, so why not start with the Harwich -Hoek van Holland ferry? That takes yopu almost straight into Rotterdam, from where yopu could head north to Amsterdam. Then south to Köln (and/or Frankfurt) and south again (via Karlruhe and/or Strasbourg) to Basel and/or Zurich. Head south-west to Geneva and onto Lyon, then head for Paris (either via Beaune, which is shorter, or via Limoges). Then back to Calais and London.
An alternative to the last part above would would be to do Lyon-Limoges-Bordeaux-Rennes-Cherbourg-Portsmouth-London.
Chris