Why not take a train from London-Edinburgh? British trains are 1st class, comfortable, and reasonably quiet. Driving in and around London is nightmarish for most anyone, even natives.

Once you reach Scotland, by all means hire a car. Better yet, either bring your sat-nav or request a vehicle with it installed. These are well worth the small expense and will save you much aggravation behind the wheel.

Also, purchase this book entitled Driving In Britain - A North American's Guide to the Ins and Outs and Roundabouts of Driving Over There.

It can be found here: http://www.amazon.com/Driving-Britai...7309724&sr=1-1

It'll make matters far less stressful - especially when you hit your first roundabout. I recommend it highly.

Slainte,
steve