This is just a suggestion, based upon experience:
4 years ago, a young friend of mine (then approaching 17 years old) was desperately trying to find a firm who would take him on as an trainee plumber. (He'd already completed one year of theory training at college but he needed to get a work placement, to learn the practical side of things, while completing the rest of his college training on a part-time basis). I drafted a letter for him which we sent to 42 plumbing firms which I'd selected from Yellow Pages. 37 didn't reply. 4 sent polite letters of rejection but one firm offered him a job.
My friend will be 21 in August. He's now self-employed, Corgi-registered and paying higher-rate tax!
So, my suggestion is go through Yellow Pages and write to every company, both big and small, which looks as if it might be able to offer an apprenticeship. I can't guarantee that this will work but, based upon my own experience, it's got to be worth a try.
Chris