An update for anyone with this problem:
Every day I have been checking my email inbox and spam folder with no sign of any serial or download link.
I have email forwarding set up (I use Gmail) to send multiple addresses to one inbox. It suddenly dawned on me that something might be going wrong with the forwarding (even though all my regular mail was coming through) so I logged into my other account and found about 4 emails from Arturia in the spam folder for that address.
Anyone that has email forwarding set up might like to check this out. It's pretty weird, as I don't have this problem with emails from anywhere else - they all get forwarded to my main address. For some (very annoying!) reason Arturia's serial/download link emails weren't getting forwarded, even though I'd received other emails from Arturia in the past.
So happy to have finally worked it out and to see that Arturia have been on it the whole time. Thanks guys
Sorry to have doubted you.