You can certainly approach your GP practice on your own - usually over the phone at the moment rather than in person, but you should be able to check this online on your GP practice website.
For people aged 16 or 17, the GP has to decide in every case whether they can take things forward without the involvement of a parent/guardian.
For suspected mental health difficulties in young people, and indeed many adults, it is often helpful to speak to a family member, so it might be that the GP asks for your permission to speak to your parents. If there are specific things you do not want your parents to know and there are no major risks involved, doctors would usually be able to negotiate with you what things they or don't tell your parents. This means they wouldn't have to tell them everything you have told them, particularly if it is very personal.
So the first step to take is to make that call, and arrange to have a chat with them. If you're not sure of the number you can google it. And it's worth checking the website first anyway as some surgeries ask you to call at specific times of day to book appointments. Or you can call them in a less busy moment - early afternoons tend to be a bit quieter - and ask them how to go about it.