Have you applied for your Class One?
If so you should get an appointment time, just like going to the doctors. If you are lucky it would be in the afternoon, although from yorkshire you will still be pushing it to get down to Gatwick, (an early start I should imagine!). The actual medical will take a few hours at most, usual stuff, eye test, hearing test, x-ray, urine sample, a few questions and an examination. Accomidation would have to be at one of Gatwicks local Hotels Im affraid. The medical centre is a short taxi ride if you go by public transport. Agrree with dave as to staying over the night before, last thing you want is to be stuck on the M25!
Goodlook and take a magazine with you!