I heard you can self refer to some GICs but the usual procedure is to visit a GP for an official referral, which is what I did.
When I told my GP she was very sympathetic, and asked only appropriate questions, referred me right away to the nearest GIC. I have since had a session there with the staff to discuss my case and will have 2 or 3 more soon. The doctor does not assess your case, they simply ask if you are sure you want to go further and speak to specialists at a GIC and if you say yes, then they will send a letter or email to the GIC requesting you an appointment. Then like me you will probably have a 10 month or so wait. The GP has no reason to ask inappropriate questions such as anything about your sexuality etc. - what questions they should ask should only be pertinent to getting you an appointment at the gender clinic. In my case, she asked only if I was fairly sure my problems were gender related, that did I suffer gender dysphoria, and that did I wish to live as a man with a male identity. I answered yes to all of these questions and she sent the referral.
Yes, it is highly confidential - as is all information that is disclosed to the GP, excluding all those who are legally allowed access to your medical records, such as certain job applications, medical specialists, etc. They are not supposed to tell anybody else, such as family members. If they do, they are liable for disciplinary action. But it will be on your medical records.
I think - given some of the stories others have told of their GP referrals - that I was very lucky. My GP is a nice person who is following up helping me regarding the trans issue with other associated medication. Others haven't been so lucky. If you suspect your personal GP will be problematic, perhaps you can self-refer.