Whether or not you pay tax on your part-time job depends on how much you earn, not on the number of hours you work. Everyone receives a certain amount of income in each tax year on which no tax has to be paid. This is called the Personal Allowance (£9,440 in 2013-2014). If your earnings from your part-time job are below this, then you do not have to pay tax on them. If your earnings are more than this, you will pay tax on the difference.
HM Revenue & Customs (HMRC) charge different rates of Income Tax depending on how much you earn. The rates for 2013-2014 are:
If you have paid tax and your total taxable income for the year doesn't go above your Personal Allowance, you can claim a refund. You can even do this during the tax year if your income is likely to remain below your Personal Allowance. If you think you have paid too much tax you should ask HMRC for a repayment claim form P50 (Opens new window).