In short, the answer for most students is: yes, can you work.
How much though depends upon your nationality and visa status. You should also consider how much work is realistic given you are studying full-time.
If you are an international student on a Tier 4 visa, you can work for up to 20 hours per week. To make sure that the university you want to study at can give you the visa you need, you should check both the Official UKVI Sponsor list and the list of 'recognised bodies'
Students who have EU citizenship do not need to apply for a visa to study in the UK and can work in the UK with no restrictions.