If you can manage to sleep on a coach, there's one which leaves Darlington at 0005 and arrives at Gatwick at 0715. Have a bite to eat and get to your Class 1; if you finish by mid-day, you can then catch a return coach at 1240, arriving back at 2025. If you're a student, it'll cost you all of £33.
More information can be found at
http://www.gobycoach.com/TravelEnq/TravelEnq.cfm
Best of luck with your medical!!