I think the guidelines changed a couple of years ago, it's much harder to get braces on the NHS now.
My DS didn't qualify but we decided that we would pay, because they were quite bad and the overcrowding would lead to problems later on in life.
We "shopped around" and had quotes for 3k, 2.5k and 1.7k. Went with the cheapest, he is almost at the end of treatment, has a permanent retainer at the bottom, and will get removable retainers made for nighttime, because it was so bad the teeth would move back. In 2 weeks the braces will come off, his teeth will get a polish and we're done.
They look incredibly good and it was money well spent. We had a payment plan, £500 up front and the rest in monthly installments of £100.
So it's not just the bits of metal and plastic, it's complicated, moulds are taken, dental lab work, the check ups with adjustments, the retainers (again, moulds taken and created in a lab).
£3.5k and 3 different braces (?) sounds a lot though. If you are in SE London, pm me for a recommendation.