There are no restrictions on working in the UK if you are an EU, EEA or Swiss national.
If you are an international student with a restriction on working in your passport, rather than a prohibition on working, usually you are allowed to work up to 20 hours a week during term time and as much as you like in the vacations. It is very important that you do not break these rules otherwise you may find you are not allowed to stay in the UK. You should check what restrictions apply to you, and seek advice from an advice centre which is qualified to give immigration advice, before you take up any work.
If you work in the UK while you are studying you will usually pay income tax and national insurance contributions in the same way as home students. For more information on international students and tax, see the HMRC guide for international students.
If you are about to leave, or have left the UK, you may be able to reclaim any tax you have paid by filling in Form P85.