Actually because locksmith apprenticeships are so rare i think you will find nearly all lockies have come from a trade, have earnt most of thier money for setting up in life (got a house, car, kids etc) and do locksmithing for enjoyment knowing they always have a backup trade.
Hey its not impossable, weve done it, if you can get the funds then give it a go but as toomush said i too would go the electrician route first even if only to get the bits of paper, locksmithing isnt always 100% full time, most of us have a side line as well to bring that little bit extra in, yours could be this whilst practiceing locks,
Another idea is that you may be able to get a grant from the princes trust or somthing for training or such like because of your age.
Think long and hard about the advice given.