if by self referring you mean going to your gp for help, then in my experience it can be an actual post code lottery.
Some surgeries will have a gp that specialises in mental health and some will not. some will have a contract with an outside company to provide talking therapies and some will not, some will employ counsellors directly.
In most cases, the gp or the practice nurse is the first port of call.... waiting times to see a counsellor or another mental health practitioner can very from a couple of weeks, a couple of months or more depending on where we live.
Charities such as Mind provide mental health support and counselling, it may be as well to check what they provide in your area and your gp may have a list of counsellors and local mental health charities.