You're going to fly into London, quite possibly jetlagged and tired, and then drive all the way to the Scottish Highlands? I'm not surprised they're reluctant to rent you a car...!

I'd strongly suggest you look at taking the train up north, and/or a flight (Virgin Little Red have some great fares in the run up to closing down). Once there, rent a car

As for renting a car as a young driver, we have at least one thread here on it from fairly recently. Basically you're probably going to want an independent car hire place, not one of the big chains. Not all will offer it, but if you ring round you ought to find one (especially one near a uni) who'll have a more reasonable young driver insurance deal