Thanks, as always, for the swift reply Jason. However, sorry, no joy!
I think the fault lies in the drop-down page (take a look at in, in beta form, in action at http://www.blendworth.co.uk/test_dynamic_dropdowns3.php).
Whilst I've amended the select field name by appending the square brackets as you recommended (name="targetList" id="targetList") it doesn't seem to be creating an array. I've modified the request method to GET so that you can see what's being sent.
In addition, I'm only really interested in sending an array of the labels the get selected into targetList and not the parentList and childList ids as seems to be happening at the moment.