I can't actually see any glue, so I can't identify it, but she's stuck fast, poor love. For all I know it could be a boiled sweet although as it's invisible, it's more than likely superglue (why would anyone want to do that to her?).
She's been in hot water for a couple of hours now (I keep changing the water and trying to move her) but there's no change, other than that I have now managed to pull her head off (but that wasn't stuck, that was just me being feeble).
Thanks for all the advice, I'll crack this problem (if I don't crack the poor child in the meantime!)