Ring up all of the jobs you apply for, it's better to talk on the phone then send an email. You could also try using a job agency, I'm with one now and they've found me some retail work at M&S. Also make sure you aren't too picky when you are job hunting. It's easier to get a job in a warehouse or retail. It's also easier to get another job, while you're in one so working a minimum wage job until you find a better one is the way a lot of people start-out.

If you are struggling to find a part time job from my prospective try look for voluntary work. When you done that it will give you better chance an employee will hire you. I know you won't get paid or anything but it will look good on your CV mate.