A large number of people in the UK will experience suicidal thoughts each year, and many more will suffer from depression. A fraction of these will ever see a psychiatrist. I believe something like one in four people in the UK will experience mental illness (including anxiety and depression) at some point in their lives. Most of these who actually seek help will be unlikely to get further than their GP.
As for seeing a psychologist (not a psychiatrist), even on the NHS, a GP's referral for someone suffering with depression is likely to be to a therapist who the surgery knows and trusts, but most of the time this will not be a psychologist.
If someone reports depression to a GP, they would of course be asked whether they had suicidal thoughts, amongst other things. Importantly, having suicidal thoughts does not actually mean the person is a risk to themselves. Only in extreme cases would a healthcare professional take immediate action, and this would, if there was a genuine threat that the individual would kill themselves, involve sectioning them. An incredibly extreme option.
Kate McCann was provided with a trauma expert immediately by a third party (Mark Warner). She obviously built a good relationship with him because she kept using him. There was no need for her to be referred to a psychologist, a GP or a psychiatrist. If she had a good relationship with her therapist, why would she move onto a different one?
