Banks are keen for the custom of domestic students as they see them as likely to stick with them for life and use their other services like insurance, loans, credits cards and such. However if you are a foreign student they are not quite so forthcoming. So for international students look at this link for relevant information.
Money guide for international students

When choosing a bank don't just look at the free gifts, check out their charges, overdraft limits, duration and flexibility. Remember if you run into difficulties, it is important to keep in touch with your bank rather than bury your head in the sand. If you contact them as soon as you realise you have a problem they are more likely to understand. The SU Advice Service is also always here for you should you run into any problems.