My livery is super cheap, even in a cheap area of the country- I feel incredibly lucky to get what I do for the price. However I'm currently paying:
DIY livery including use of school and hacking on their land- £95 a month.
Haylage from farm- £30 a month in winter (option to buy in hay for closer to £40 a month).
Bedding- £50 a month(ish) (this has really shot up this winter and I can't use straw because it makes my pony cough).
Insurance- £110 a month.
Feed inc supplements- £20ish a month in winter.
I try to set aside a further £30 a month to go towards less regular costs like dentist, vaccination, saddle fitting, worming etc.
Farrier- Fronts and a rear trim £48 6-7 weeks.
So let's say my base costs per month are about £370 a month. By the time you add in petrol to and from the yard + occasional paid for help, probably call it £400 a month as a round figure.
This is for a very cheap to keep cob type who mostly doesn't require expensive feed, regular vet visits etc.
However, on top of this I would say there are additional yearly costs.
I would say every year I easily spend £500 on "stuff"- this could be anything from a new rug, new saddle pad, various sprays, shampoos, grooming kit, replacing things he has broken... £500 is probably a very conservative estimate, and in the first year it was definitely more. Most of this is not essential, although some of it e.g. water buckets, fly spray, basic grooming kit probably are. However, if you are constantly having to pinch pennies and go for the cheapest of everything, it's no fun.
Add onto this probably at least one emergency vet visit a year, just because horses are like that.
I doubt I am realistically getting much change from £5,500 a year. And as I say, this is a cheap pony in a cheap area of the country. Yes, there are times when I could probably save a bit of cash- I pay for help with clipping for example, which isn't absolutely essential, but I'm bad at it, and it's nice to have someone else do a nice job! But I'm also genuinely not being extravagant, and a lot of my feed etc are cheaper options, and fed in small quantities, especially in summer.
And we haven't even really talked about additional spends to really enjoy your new horse/pony.
Obviously lessons etc aren't essential, but I like having them and going out and doing things where possible.
Currently, I probably have about two lessons at home a month from a lovely instructor who teaches a few of us at the yard. She charges £20 for a shared 45 minute lesson, which I think is very good value. I also am lucky enough to be able to go out to clinics occasionally, which usually cost £30-40 (or more depending on who is teaching) + petrol money for the driver.
I do think as a new horse owner, you have to factor in the cost of some professional help, although the actual amount you need will vary. Your teens may also want to compete etc which can get very expensive very quickly!
I do know people who do it more cheaply than me at basic grass livery with no facilities, horses living out all year round etc- which does save on costs a lot (no bedding and less hay to factor in usually, too) but equally it can be very miserable in the winter!
Around here, I would say if you can budget £6000 a year, you can afford it on DIY. I don't know if that would be possible in the SE or in a less rural area.