The only way you're going to get a part-time job is if you
put the effort in. Most places don't advertise part-time jobs, you have to go around stores and hand in your CV to them. So you need a good CV (aka "resume") with a good covering letter. No crappy Word-based template, that's not going to stick out from the other 100 applications. I made mine in Photoshop. Look it up on Google.
Are you in secondary school still? Like saralk said, when you start going college, depending on your household income, you can receive up to £30 a week with EMA, and £100 bonuses twice a year I think it is. I get £10 a week *sigh* and should be getting the January bonus soon.