Oh that's not good. It wasn't that simple for me either though everyone I spoke to was clearly trying to help.
First I went to the apple support website and initiated a chat. She told me that she wouldn't be able to deal with the issue directly so would arrange for the senior advisor team to call.
They called while I was still in the chat but I wasn't put through to the senior advisor team. I presume the lady I spoke to there was a regular AppleCare advisor. She said that I would need to speak to aftersales and was about to put me through when she noticed the notes from the chat.
So instead she put me through to this guy in the senior advisor team(Ireland). He told me he was going to take ownership of the case until its resolution but then he put me through to aftersales. So that step was a bit of a waste of time but I do have his phone number and he said to call if I have any issues.
So then I spoke to an American lady (but who's to say she's not based in Ireland) who set up the replacement. She said the courier would call to arrange pickup within 48 hours and then once the phone was received they would send the new one out within 3-5 days. This person works in apple distribution international according to her email sig, not sure if that gives a clue as to where she's based.
I contacted aftersales directly today to ask if I can keep the old phone until I receive the replacement and was told yes and that I should arrange the return of the defective unit once I receive new one.