Yes, I'm afraid that CVs just get piled up and lost - there is an element of luck about seeing a vacancy as it occurs.
ds & dd Job 1. - delivering the free paper each week.... just had a look in the paper for the contact details and asked how to apply to deliver it
ds Job 2 - working in a local shop, cleaning..... happened to be with his mate on an errand for mate's Mum and chap behind the counter asked if either of them fancied a few hours work each week this is after much nagging from me saying a job wouldn't just come up and offer itself to him 
ds Job 3 - A friend who manages a shop where they like to recruit people who know stuff about the product they sell (for example, thing if it were a fishing shop, they like to employ anglers) asked him if he was interested
dd was also asked for Job 3 on same basis, but turned that one down.
dd was asked by the company where she did her week's work experience at the end of Yr10, if she'd come back when she was 16
ds & dd Then took a lifeguards course and work at that now, for better pay (do have to pay for course up front, and, of course, have the swimming skills, pass the tests, etc)
All the teens I know who have work, have just 'happened' to be in the right place at the right time, (except where have a specialist qualification) tbh - just 'happened' to have been asking at the employers place when they needed someone, rather than handing in a CV and hoping.
You can sign up to Indeed.co.uk for your area which advertises PT jobs.