Hi Samantha,
In it's baldest sense that is exactly what you need to do. It can be a bit of a hurdle knowing how to start, but I found once I got going I couldn't stop.
May I make a suggestion? In order to give yourself time to discuss this fully with your GP, it might be an idea to book a double appointment - that's what I did and I was glad of the extra time. You might also want to take some information with you about NHS options for transition - you can find some stuff on NHS Choices
Your GP will refer you to your local Mental Health team so that hey can screen you for other undiagnosed conditions which might need to be taken into account or which might mimic Gender Dysphoria. This is not a "gatekeeper" situation, but a positive step to ensure that you get the most appropriate care.
You will need at least two visits to the Gender Identity Clinic before they start prescribing Hormones - the 2nd visit is with a different doctor to ensure that the diagnosis is correct and the proposed treatment regime is the best one for you.