Declined student overdraft

Ok, well basically I got accepted for a co operative student bank account a few months ago but I missed the deadline; so I did it again and I left it as I thought I wanted to go with another bank again. Then I applied again a few weeks ago (stupid I know) but I got declined based on my credit score. I've recently opened up a student bank account with natwest and when I've got to apply for an overdraft I've been declined. Now is this because of applying for the co operative too many times? I feel stupid now as I could have probably prevented this. I'll be living off £20 a week when I move to university until I can find a job and I just feel like I'm going to struggle. Is there a way to improve my score?