As above, your age is irrelevant when it comes to determining how much, if any, tax is due on your income. If you earn more than your annual 'personal allowance' (currently £6,475 for most people), you'll have to pay Income Tax on your earnings in excess of this.
In the UK, a system called 'Pay As You Earn' (PAYE) is used to collect Income Tax from employees' salary. This system relies on a 'tax code' to apply the correct personal allowance to each individual, and if you don't give sufficient information (usually from a form P45 or P46) to your employer when you start working for them, it's quite common to be put on a code that gives a lower personal allowance than you should have.
I'd suggest checking your payslip - if the code is "BR" and you only have one job, this is most likely incorrect; a "647L" code would indicate the standard personal allowance is being applied. If you are on the wrong code, the easiest way to fix this is just to call your tax office (contact details
here) and explain the situation. They should be able to issue a revised 'notice of coding' to your employer to amend your tax code, and you'll then receive a refund of any overpaid Income Tax the next time that you're paid.
If your tax code doesn't seem to be the problem, it would be useful if you could post details of our cumulative income to date in the current tax year (i.e., since 6 April 2009), as well as your level of weekly earnings, so that it's possible to work out what tax you should be paying.
Also, note that you
won't be able to reclaim any National Insurance Contributions (NICS) that you've paid (these are also collected via PAYE). The tax-free threshold for NICS applies for each pay period rather tha for the tax year as a whole, so you can't get a refund on the basis of your overall level of annual income.