My wife works in the NHS at a mental health unit and I work in science with many NHS doctors.
1. NHS staff do generally get paid a lot less than in private health care, so much so that there is a shortage of staff doing the skilled jobs such as psychology and clinical psychology
2. There is a phenomenal amount of waste because you get managers who piss away their funding and they don't care since they hold permanent positions (which is a waste of money in itself), lots of underfunded services around the UK
3. People underestimate the cost of providing medical services for "free", the maintenance on medical equipment is a lot, services for mentally ill is a lot and that includes kids that are abused, eating disorders, suicidal people, etc.
4. The waiting list where my wife is to receive treatment is a year, if you're a kid being bullied it's a lifetime of struggle unless you've made an attempt on your life to get moved up the queue. It's very sad really and there is a pressure to discharge people. Also, people with mental health issues lie like the killer, but you can't spend millions to monitor this one guy all of his life because he might stab someone, it's not feasible.
5. Doctors who get paid a lot have done many years of hard graft, a junior doctor gets nothing but for their career will have to work stupid hours to climb that ladder. Also, don't discount the mental stress and pressure to never make a mistake or get a complaint because it can end your career in a heartbeat.
6. People do take the piss out of the system. Getting drunk and ending up in A&E because of stupid stuff costs a lot, and they won't be sent home unless they're fixed ie, they break a bone and have x ray, get a cast, get medication, follow up, physiotherapy, etc. Others will demand a mental health diagnosis so they get financial benefits or that they're shitty parents who blame their child's abnormal behaviour on autism or something, rather then them having to raise their kids properly.
More complex than people believe and no easy solution.