@Needanewname42 okay, I thought I did know where to go but they'd gone elsewhere. With me I think It's that I just don't want something else to look after-I work part-time (30hrs) as well as having private clients and a business to run, and I go away a lot (single and without children) and have a large dog to facilitate into life-and I just don't want anything else. Maybe one day if things are different.
The teens on this yard are always so keen for anyone looking to get their own horses-they form an orderly queue to be the one who helps look after them, that I have noticed!
That's interesting @maxelly
Yes, a lot of 'horsey people' are just that aren't they. I guess running the riding school is their means of having the money to just do 'horsey' things. I had found this one much, much friendlier than a lot of them I've attended, I will say-some are so snotty!
I am really not bolshy especially in situations like this where I don't know anyone well yet. I do like the school so I will go back. And I will post in the tack room in future. I guess I view that as a bit like 'the litter tray' or 'the doghouse' , for owners or prospective owners of the animal largely. It is a good point! I do that with people considering getting dogs (trying to put people off getting one unless conditions are perfect)!
@FieldInWhichFucksAreGrownIsBarren I know, I should have said something to the kids, I realise. I just don't like asking children 'adult' questions generally. And I do think the one left in charge should have said something and/or been told to keep a look out for me if the other riders had all beggared off elsewhere before 09:30.
There's always been someone in the office when I've left, in fairness-usually the instructor who's done this lesson will go in there and then they ask if you want to book in your next one. If you're not sure if you can attend next week or aren't able to come for a while, you just contact them to book in via their fb page to book in.
There isn't an app as far as I know.
I have noticed that @maxelly , about non-updated horse names on stables, in every school I've attended, and same with boards/notices! I understand it-I am not the most organised person myself, you just can't rely on that sort of thing. Same with 'Which horse am I on today?' 'That one over there, the one with its forelock out and the patch on his side-'Er yes, that's like, five of them' 
I was also asked to take the horse I'd ridden to his stable and plait his reins, one time recently. Fine, I know how to do reins and I knew where this horses' stable was, but what if I didn't? I'd never seen this person before so they'd no idea-I could have never ridden a horse before in my life up until that lesson for all they knew!
Also the first lesson I had here. They asked upon booking if I'd ridden before, that's it. And then they went straight on to cantering and jockey position. What if I hadn't ridden for years, was nervous, had only ridden once and didn't know how to do it/fell off? 
I am not complaining, I do like this school a lot and the people generally are good.
It's nice of you to be so helpful but as you say, you're also a 'customer', you're not an employee of the school!
Anyway, they responded to my message protesting that I was present and correct, and that I had had lessons in different places, and that I was there earlier than 09:30 etc etc.
They've said they'd honour it this time as a misunderstanding. They'd spoken to the girl who saw me-and did I want to book in again. I have said yes, and that I'd pay half the lesson price next time I pay, that's me taking heed of these replies, yes I could have gone looking for them (although I'd have found that quite embarrassing to have to do) and yes I could have asked the children.
Money aside, I was quite upset at missing that lesson as I do love riding, learning and horses. Also, I was knackered and would have appreciated a lie-in that morning rather than having to get up and walk dog and rush off as I have a busy day ahead and had worked late the night before. But I still booked as I really wanted to go, so it was disappointing to get there and not get to ride. Just a pesky situation all round.
Thank you for everyone's input! 