Probably a bit late now but the links above aren't as helpful as they could be.
Private Coach/mini-coach will take at least 3½ hours to Exeter from LHR, probably over 4 hrs. To go to the Exeter side of Dartmoor will be the best part of an hour, longer from EXT airport. I wouldn't bother using fixed wing (you'll still end up with quite a drive), shortest duration will be by helicopter (2 for that number of pax) and will take about 1:30 hrs, and will be a lot less hassle.
Try one of the Charter Heli companies nearest LHR such as
PremiAir