I'm in a similar situation with age Martin, in so much as I'm 17, but turn 18 in April, which is during the training courses for the handling agents that I've applied to. So far, it hasn't posed too much of a problem, as I'd be 18 by the time the job has started, but I've heard of handling agents hiring people who would be turning 18 within a few weeks of the job starting. The issue as Louis has said, is not only getting the airside security clearance, but also there are legal restrictions which prevent a company from working you 24/7, I believe they can only work people aged 16/17 between 05:00 and 23:00.
It's probably worth trying your luck anyway, because some companies more than others are desperately under-staffed in the summer. I'm lucky to have quite a few GCSEs and A-Levels under my belt, but at both interviews for handling agents, whilst these were viewed impressively, they said they were more interested in personalities than grades, as they're looking for people who can do the job well.