If you’re not interested in salmon, then a 9’ 5wt rod will do everything in the UK.
There’s a Chinese knock off brand called Maxcatch that sells on eBay and Amazon - they seem to rebadge previous seasons models from the big brands and sell them on. I have two of their rods, and they’re as good as you need. Or Shakespeare do entirely effective rods for sensible money.
Reels, as said above, are just somewhere to hold line. Any will do provided they’re the right size.
Flyline - doesn’t really seem to matter if you pay £15 or £80. I currently have a 10+ year old line that is cracked and rough, but it does what I need it to. So I don’t think paying a fortune for some ultra slippy super duper line makes much difference. Though when you’re starting out, I think it helps a lot to have a very aggressively front loaded weight forward line, or get a line one size heavier than the weighting of the rod.
Leader - I have 3 spools (8lb, 6lb and 4lb fluorocarbon) from a bargain bin at a fishing shop. Again, I don’t think it really matters much.
Would highly recommend getting yourself a maxcatch "gold" line. not quite as "slick" compound as the Rio gold lines, but otherwise identical in profile and casting.
I would recommend the Shakespeare oracle range just because you would be able to get into a store and see/feel what you are getting - the MC stuff is good as well, but there are so many options of rod that you're liable to confound yourself.
The usual advice is a 9ft 5wt rod for river fishing, and a 10ft 7wt rod for fishing stillwaters/commercials. If you look for second hand, you probably should be able to get yourself one of each if you are still not quite committed to fishing one or the other

(Caveat on the 10ft 7wt, if you are fishing very small stillwaters, you may get away with the 9ft 5wt, but you will still feel undergunned in the most part).
Leaders, you can get some decent tapered leaders (quite helpful) off amazon for not a lot of money. Put a loop in at the end of it and then attach your choice of fluorocarbon or nylon (I personally use Maxima clear or chameleon). The tapered leaders to help with your fly turnover, but they are not "essential" - I think I now actually use furled leaders on all my trout gear (not that I've been out for trout in ages, mostly stick to salmon nowadays - hence the profile picture).
Reels, agreed as above. Unless you're going to places like Sutton springs or Ledyatt, you will never realistically need a superduper drag system. Most fish you'll be catching you will end up playing them by finessing the fly line.
Buy S/H as there is always good kit for sale, I would suggest going for old Hardy/Greys/Sage/Orvis rods and reels.
Dont skimp on fly lines! buy decent ones but no need to spend the crazy £80+ unless you are planning on trying competition casting!
I have used Vision waders and boots for years, very very good, I get 2-3 seasons out of mine and I am a big lump crashing around undergrowth and over fences!
Flies, well I have boxes of them but always go to the same half dozen or so for rivers and small still waters.
Dont overthink fly choice! If trout are hungry and not in fear of their lives they will eat anything that resembles food.
Enjoy! Fly fishing is even better than shooting! (as long as its warm, the rivers arent in flood and/or full of sewage and not its not windy!)
If you do go river fishing, I would 2nd the recommendation for the Vision waders (I think the model is Koski). They're not the cheapest/entry model, but they have done me quite a while and everyone I know who has a pair says the same thing.
I would contact a chap called Dave Gordon who runs Diver Dave's Wader Repairs up in Aberdeen. He usually has a decent selection of warranty replacement waders (from a variety of brands/budgets) to chose from, and can also offer a decent discount on a new pair - he is the chap that most of the companies send their warranty returns to to get repaired. (I will say, you can read hit and miss things about him on the internet, but I personally have had very good experiences dealing with Dave)
Final bit of advice - NEVER, and I mean
NEVER decide to take up fly tying in the thought that you'll "save money". Yes, it is cheaper for me to have tied up all the flies that I have in my boxes (and given away) than it would have been to buy them from a commercial tyer. But as CreedSnore said, you end up going to your auld favourites time and time again. For me, thats a Kinermony Killer for the salmon.