As an International (non-EU) student, if you have student immigration permission that allows you to take employment, you can work up to 20 hours a week during term-time. This depends on when you made your immigration application, where you are studying and the type of course you are taking. You can work full-time during your holidays and on work placements. For more information, please visit the "Can you work?" section on the UKCISA website.
If you are an EU student (except Croatian nationals), then you are eligible to work in the UK without restrictions. Croatian students need to obtain a yellow registration certificate to work legally in the UK. You can then work up to 20 hours per week during term time and full-time during the holidays. In order to apply for the yellow registration certificate, you need to complete the CR1 application form available to download from the UKBA website.