How Should I Start?

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Hi,

I live in Glasgow, and I am waiting for NHS to send me a letter and tell me when I'll be able to see my surgeon.
But I'm tired of waiting and I want to get the surgery done this summer.
So I guess I should see some private doctors about it.
But how should I start? who should I see? what kind of doctor does this job? Do I have to see a consultant first or can I start with a surgeon?
How long will it take to do the job if I want to do it privately?
and does any of you know a good surgeon in Glasgow?