Parents won't let me go out to London?

I'm 16 and my parents won't let me take a direct 30-40 minute train out to London. I know they care for me and don't want anything to happen to me (I'm the youngest sibling), but there's only so much in my greater London area to do with friends. I have been asking since I was 14 and the answer has always been no. I've had to turn down so many invites as I'm not allowed to go out that it's becoming increasingly troublesome. It's gotten to the point where I just reject the invite and don't bother asking as I know they'll say no and a lecture will be imminent.
How do I persuade them to let me go out?

Maybe if you ask them to let a sister or brother accompany you the first time, so you know your way around? That way they know your still safe and they'll be certain you know where your going to and back. Hope this helped