If you are imminently suicidal, you can be hospitalised but there is little to no support outside of that. Bluntly, there are a lot imminently suicidal people and limited resources. If you attempt to commit suicide and are unsuccessful, that wouldn't speed up the process.
Also, it is worth saying the rate of suicide in Scotland is very high. I live in a small place in Scotland with essentially no poverty, and there are still 10 or so suicides every year. I know someone who works as a psychologist within the NHS in Dundee (probably one of the worst cities globally for suicide/deaths of despair), and it is totally out of control. There isn't sufficient funding, and there is no way to acquire sufficient funding...it isn't possible (and btw, it isn't just suicide...heavy drug use in Scotland has been an issue for many decades).
The level of underfunding is, however, such that mental health providers are a huge part of the private health sector: Priory Group is a very big one.
Another factor is that a lot of training for psychologists is paid by the NHS, and funding for training has been going down everywhere (even in Scotland, which has a left-wing govt running the NHS).
It is just a resources problem. Even in the private sector, there isn't a supply response to higher prices. Ironically, the UK has lots of people who do undergrad Psychology, just none of them actually go on to practice because entry is so tightly controlled (for some reason, the NHS in Scotland is attempting to train nurses to do psychology with a couple of days training...that is going as well as you can imagine).
I understand no-one in the US wants to hear it...the UK system doesn't work (fully public health doesn't work, almost no countries in Europe with good healthcare have it, Australia is very similar to the UK, introduced private healthcare...their results are miles, miles, miles ahead).