Hmmm... Now I'm even more confused.
I've just tried all the accounts again and all are working apart from my main personal one (GMX using IMAP). I was sure I'd had the timeout error with the pop accounts but now I'm wondering if the error just happened to display when I was looking at the pop account and actually referred to a sync error on my GMX
I've tried deleting the accounts and have also done a factory reset but its still the same.
The settings I'm using for the GMX account are the same as on my old phone:
Server: imap.gmx.com, SSL, Port 993
Outgoing server: mail.gmx.com, SSL, Port 465