Perhaps there is a pleasure ride you can start out with? I haven't done endurance in this country but I would assume there are 'short' rides from 15-30 miles or so.
If you do a short distance in a slow tempo I don't think your horse needs to be particularly fit at all.
There might be a target heart rate for your horse to have after you have completed the ride. A fitter horse will have a lower heart rate. Walking a bit at the end will also help lower the rate.
For longer distances both horse and rider needs to be fit, as the riders tend to get of and jog quite a lot!
Hi I started last year and love it! Have a look for some pleasure rides near you through either www.endurancegb.co.uk or www.sportendurance.co.uk first. They will have rides of 10 miles upwards at pleasure ride level. They still have to completed in a reasonable time but very doable. In terms of fitness you need to build up your horses trot work steadily as this is what you will complete most of the ride in. And get you horse slowly conditioned to doing three quarters of the distance you want to do a ride at. I would aim at getting your horse fit for a 15 mile ride to begin with, even if your first ride is only 10 miles. You don't need to do miles and miles, just get him/her hacking fit and happy doing 10-15 miles mainly in trot and you will be fine. If you have some good hills near you get up and down these as they are great for stamina. The rest you will learn when you join a group and start doing pleasure rides...as I did. They are a friendly and helpful bunch!
As posted - www.endurancegb.co.uk - is the place to start, or there may be a local long distance group near you. Pleasure rides are between 10 and 20 miles, competitive rides are 20 miles up to FEI rides which can be 100 miles in a day! Any distance over 20 miles requires your horse to be vetted before and after the ride, however EGB pleasure rides require that all horses must trot up for the vet before and after the ride. The best way to get your horse fit is plenty of walking. Some horses prefer to canter rather than trot where the going allows, so it all depends on your horse. As you live in a hilly part of the country - you should have no problem getting your horse fit. There was a good article in Your Horse about getting into endurance riding, it was well worth a read.