Snadger, I had a hunt around and I've got a recipe from my mother that asks for something called 'jamaica ginger' I think this is what you're looking for. As far as I can remember it came in one of those little bottles like essences and you could use it to flavour things. Stretching my memory, I think my mum used to make it with yeast in which case it would ferment and without when it sounds like your cordial.
I tried two health food shops today, in one I got a very blank look but in the other (a small independent one) the lady told me that you could only get it 'up North'. I'm going to see if I can track some down as I would like to have a go at the ginger beer. If I find any I'll let you know.