I think the thing is that you have to be aware that there are always two sides to each story.
Your dad is probably motivated not by a desire to stop your fun, but because he wants to protect your money and therefore your future.
So why resent him for that?
To further what was said earlier, you've gotta show some serious maturity to win your father over. It definitely is a bitch trying to relate this kind of thing to people who don't understand it - so you mentioned cars, find some common ground and recreate your situation/dilemma in terms he can understand and empathise with.
Just because you've spent a lot of time on this forum, and a lot of time thinking over what you want, does not simply entitle you to the pickup. That's life. So don't beg or argue with your dad, just calmly and maturely state your case.
PS. Did you earn this money yourself? If so, bring that angle in. Say that you appreciate he is looking out for you but ultimately it is your money and it is yours to spend therefore. If you make mistakes, you are young and we all learn from mistakes. It is better that you learn about handling £100 correctly when you are a kid, than never have that experience and screw up with £1000's when your older.
If he trusts you, if he respects you, and if he wants to develop your own sense of personal responsibility, then he should let you invest this time.
Good luck.