Can I get into finance from an avarage uni?

I am studying accounting and financial management at University of Hull, I am scared that because I am not at a top uni I won't be able to get any spring weeks this year or internships next year. I have some relevant experience and actively trying to get more through volunteering, doing online courses etc. Am I trying to do something that might me impossible? Will I have a chance of getting an internship/a graduate position? If no, what are my other options?