I have to tell you these jobs are very few and far between, not the least because heavy haulage, because that's what this is, is in decline. Other than that, drivers just don't have mates. Also, that natural progression from mate to trainee driver hasn't been there for many years - my husband drove in the 1970s and 1980s and it was virtually non-existent then.
What you could do is look for work as a van driver (although it's not brilliantly paid) through agencies, as Eddie suggests, or get yourself some warehouse work and let them train you on forklifts. My son doesn't have a driving licence, but makes a good living loading up lorries with a forklift.
You're unlikely to find an employer who'll train you. Your only option is to see if you can afford to take out some sort of loan and get yourself trained. Then it's back to the agencies to get yourself some experience.