dh (Armed Forces) and I (state school teacher) sent ds to prep; it cost about £10k a year. We didn't get help from the MOD, as ds wasn't boarding (there are very stringent criteria to get help with day fees), and also I wasn't mobile (I chose not to move around every 18 months with dh).
As dh was away during the week, and for two years was abroad and I was in Cornwall, prep meant that I could drop ds off for breakfast at school at 0750, and pick him up after supper and prep was done at 1850. This meant I could work til 1830 on 4 nights, as he finished at 1600 on a Wed and also went to school on Saturday, which meant that Sunday was a day for just us, as on Saturday I'd sorted domestics and done planning and marking for the following week (in theory).
The help that the Armed Forces get is to provide continuity of education for your kids as changing schools every 18 months isn't clever, especially when you get to year 9. You either have the choice of sending them to board, or spending long periods of time apart from your wife/husband, perhaps leading to marriage breakdowns, and that costs more in the long run. The allowance is currently about £5k per term, and is reduced by the amount of any scholarships the child may win. I also think it's taxed, but I'm not sure as we've never claimed it.
We chose to go without flash cars and expensive holidays to do this, but that was our choice. It also meant that if I decided to move with dh then ds could board in a familiar place if necessary. In the event, ds and I also moved abroad,and ds attends the local international school....not because his prep was bad, far from it, but because we'd had enough of being apart.