Have a look at EGB website and then find your local group. They will run training/social rides throughout the season as well as competitive rides. The training rides start off with distances of 10 miles +. If you are hacking your horse out 3-4 times a week and go for a 2 hour hack at the weekend which includes trotting and cantering, then she/he will easily be fit enough to start at the lower level rides. These will give you a feel for it - if you like it and want to have a go at a competitive ride, then EGB run a scheme whereby you can "try before you buy" by having a go at a couple of competitive rides before you actually have to join EGB. If you volunteer to help at a competitive ride (and you will be very welcome), you will see how endurance riders look after their horses with their crews during the ride, and the vetting etc. Give it a go, most endurance riders are a friendly lot and will be only to happy to help someone starting off in their sport.
I am a member of both groups above and it is great fun! I would advise that as above, you need your horse to be happy doing a good 2 hour hack with plenty of trotting and some canter work. Do plenty of hacking out rather than school work and only ever increase distance or speed, never both together when training. Set yourself a training schedule where you increase things over time.
Most pleasure rides are up to 15 miles and you should be fine, it is not a race after all. Have fun...it is great. Might also suggest you go with a riding friend the first time unless your horse is used to horse parties and horses passing you and overtaking at walk or trot.
I'll probably end up at some of the some rides as you this summer then because I think we are quite close from some of your previous posts. Do come and say hello if you see a mad coloured
i would love to do some endurance too at some point, dont know whether it will be this year as i am wanting to breed my mare, but maybe once the foal is grown i may do it with them, being as i love long hacks, seems like the perfect extension