When I was 14, I didn't even have a computer. It was almost towards the end of high school when I got my very first PC. Have you talked to your parent about it and see if they can help you find a part time job, so you can earn some money for your new computer. Also try asking your school to help you find a part time job. maybe they have through some special program or something. Well that's what I did, so my parent really didn't give me money, I earned it myself to buy my very first computer.
About OP's budget, the reason why I mentioned his parent can get it for him is, first of all he's only 13 and for a 13 year old who has £300 to spend on a new computer is impossible. £300 isn't US dollars that is £300 pounds, converting £300 pounds to US Dollars comes out to about $500. A 13 year ld with $500 to spend, where do you think he gets his money from? Who knows maybe he has a part time job and earn it, or maybe through allowance or given to him during holidays or birthdays?
If OP at that age has that much on his own, then maybe asking his parent to buy the OS for him, won't be a problem.