Anecdotally, my wife was diagnosed in the US with sleep apnea about 2 years ago. This included multiple GP visits to even get an at-home sleep study that came up negative, us having to purchase an additional at-home sleep study out of pocket that came up positive, and an overnight sleep study. The overnight results gave a diagnosis of severe sleep apnea. The entire process from start to finish took at least 3 months.

Her insurance fought every step of the way, despite having half-decent insurance as a hospital employee. They claimed that her BMI was not high enough to have sleep apnea, and ignored the family history (both parents, 3 grand parents, one sibling, three cousins).

In the US, I went in for a sleep study and had to fight for it. "You're not obese or old" yes but both my parents (admittedly old, but not obese) have CPAPs, and my wife says I stop breathing at night. "Are you sure?" Well, sir, that's why I would like to do a study.

I had an overnight sleep study scheduled several weeks later, during which time my insurance provider at work changed, and I had to do the process again, and this time only got a take home kit, and just missed the criteria for getting a CPAP.

Years later I went looking for alternate routes, which means paying out of pocket for a CPAP and accessories... But sleeping better and being more healthy.

Isn't a full sleep study test pretty expensive in the US?

I went to a sleep specialist once and the cost of a full overnight polysomnogram was nearly $3000.

I opted for a much cheaper at home test from my GP. Showed no signs of sleep apnea but I worry about the accuracy compared to a full study.

They do. You just have to either pay for one yourself or wait half a year (or maybe way more?) for NHS to provide it.