The 'bare bones' budget just above really is bare bones. For someone to be budgeting just £15 per month for hay means they are only getting through 3 small bales of hay a month at current prices. My horse would get through a bale every 3-4 days in the winter and about a bale a week in the summer (he gets a slice in his stable no matter how much grass in order to stop him being bored, and we travel more in the summer so hay taken to shows etc.)
I keep my horses at home so don't have livery fees, but what I save in livery I spend in fencing, fertiliser and grass seed in the spring, hedge trimming etc. Land costs money whether you are renting it or owning it.
I'm all for encouraging people to keep a horse on a strict budget, but you do need to go into it with realistic expectations. The first thing that jumped out from your OP was that you wish to a) be barefoot to save money and b) go hunting. The two things are incompatible. You might manage to find the only person on the planet who does hunt barefoot successfully, but for a regular hunter you need shoes. Just the amount of work needed to keep a horse fit for hunting will wear their feet down. A friend of mine decided she was going to go barefoot and still hunt. I remember spending ages with her every time she went out looking in the deep mud for her very expensive boot that had come off within 6 minutes of leaving the meet. Every time! Even if you decide to no hunt, correct nutrition for barefoot horses and a decent barefoot trimmer trimming your horse's feet at the correct intervals, plus the expense of the boots for if you do need them to ride in, will not come in much cheaper than shoeing. And it will limit the horses you can look at. If you keep one thing in your budget, I'd make it shoes - no foot, no horse it the old saying.
As to livery costs - you can do things the 'lots of money' way or the 'lots of work' way. True DIY livery can be found for less than £120 a month for just a field and stable, but don't underestimate how much work you have to put in yourself. If you go to a yard where they have a school, with lights, and a groom who will do the odd turnout for you, the price will be higher but you life a little easier.
Feed is a massively variable price, and will be hugely affected by the amount of work it does and the type of horse it is. My horse (small Irish cobby thing, hunts twice a week in the winter and does long distance competition in the summer) is not a good-dooer and works hard. He gets whatever he needs to keep him in top condition, but I've still searched out the most cost effective way to do this. Per month he will eat on average a back of basic sugar beet (£8), 1-2 bags Alfa-A (£12.50-25) and 2 bags of Top Spec Turbo (£28.) I tried him on straight oats and micronised linseed as that would be cheaper but he likes the Turbo best! So I can keep a fussy horse hunting fit on simple feed for about £60 a month. My daughter's pony (14hh Welsh Pony Clubber hunting weekly and doing rallies and shows in the summer plus a few long distance competitions) makes much better use of his feed and gets through a bag of Allen and Page mash a month at £14. We give him a handful of Turbo the day of a show to wake him up a bit. And that's all he needs!
Decide early on how you are going to deal with vets fees. Make a plan and stick to it. You can pay insurance but if you are keeping costs down don't be suckered into paying for loss of use. Alternatively start with a contingency pot and add to it each month. Put it somewhere you can't get at it, even to borrow a bit from it. Colic surgery can cost £5000. I bought a young horse, put a bit of money aside each month for him and after 2 months of owning him (when I had a contingency pot of only £60!) he was diagnosed with a very rare malignant tumour which cost £3300 to fix. Otoh, my previous horse had cost me £6000 in insurance premiums over the years I'd owned him and I only ever claimed treatment worth £200. Imagine if I'd put that in the bank!
So after livery, feed, shoes and insurance/contingency, you've got bedding, routine healthcare, equipment and fun to pay for. Bedding is going to cost you about £30 a month in winter if you use shavings, pellets, hemp, etc, slightly less in summer, if you are careful and frugal with bedding. The only way to get it lower is with straw. I tried straw as an experiment last winter and rapidly went back to pellets! Far too much work and stinky as hell! Routine healthcare - check with the local vets for if they do free callouts for routine work in exchange for you being flexible. Mine do free visits on a Tuesday but you have to take the time they give you, but I get all the teeth and jabs done at the same time once a year. Everything is cheaper (saddlers, physios, vets, dentists, etc) the more horses they are coming to see so team up with other liveries if you can. Equipment - buy a single good quality bridle that you like. The difference between a good one and a crap one is only about £50 so buy a good simple cavesson bridle in good quality leather that fits and only ever buy one bridle. Buy a decent saddle that you find comfy and look at adjustable ones (Kent and Masters are very good.) Then when the horse changes shape you won't have to shell out for another one. Buy a decent rugging system and maintain it, and you won't need millions of rugs even if your horse lives out. Each of mine have 2 Premier Equine outers and a set of liners, and a Thermatex. Expensive rugs, but I don't have dozens of different weight turnouts and stable rugs and a thick fleece and a thin fleece etc 
that some people seem to accumulate. 3 rugs per horse and a couple of liners. That's it.
Which brings us to 'fun.' Hunting is awesome. It keeps me going though the winter. I have to go and muck out 3 in this wind this morning but it's OK because it's hunting season! If you hunt you will need to either subscribe (£250-1500 per season or more with a fashionable pack!) or buy tickets (ie buy a number of days out in a bundle.) It is possible to just pay caps, but many hunts will frown on a person who turns up sporadically through the season and doesn't commit to support the hunt. However it is acceptable to be a serial visiter and go for a couple of days each with a number of different hunts while you are starting out. You may like the long days and steadier pace of foxhounds, or you might prefer the manic pace of drag hounds. One pack may jump lots, another might gallop a long way to avoid a fence! After a while you'll find a pack you like and then a sub is sensible. You'll need good transport too for hunting, so figure out where that is coming from. You'll need transport for most outings though, but that's something that can come later. Fun though can come in all shapes and forms, but most of it costs. Competitions, fun rides, lessons. Worth considering because everyone starts out a happy hacker and eventually wants to do a little bit more!
One final thing to consider (and to keep from your husband) is that horses expand to fit the budget available. I have 3 and am considering a 4th because my kids ride too and it's not fair for my little horse to have to do all the hunting and competitions (I was 2nd in a national final on him last year) and my daughter is eyeing him up for schools showjumping too! He needs back up! We stay away a fair bit now so the trailer will soon need upgrading to a lorry. And I just started out a happy hacker too 
. I also have a friend who started out with one brown cob and kept buying horses that looked the same so one was always in the stable and the others in the field behind the big hedge. She got more and more successful as a show horse owner (eventually winning HOYS) that by the time her husband noticed she'd bought a grey hunter she actually had 3 brown cobs and 2 grey hunters!