International student as in non-EU?
I think generally any company will hire the best person for the job. If you have the right to work in the UK, I think it's illegal for them to discriminate against you based on your nationality. However if you need them to sponsor you to be able to work here, it means you might have to go further than the average candidate to prove that you are worth it to them.
Where I work, I reckon about 30-40% are not from the UK. However the vast majority of them are from the EU.