With a gmail account it takes on average 2 minutes to send mail to another gmail account. The delay from other clients seems to be around 30 sec.
With another mail account connecting to a private mail server (with SSL and port 587), the delay varies from 4 minutes to over 100 minutes, and the longer delays always occur when several test emails are sent in a short space of time.
These delays occur regardless of whether there is a 3G or wifi connection.
From what I read there is a lot of icloud stuff going on in IOS 7 and I suspect that this is the reason for the sending delays. I have an icloud account set up but the features are all disabled except for find my ipad.
I have two ipads and they both behave the same.
Grrrr. I have wasted so much time on this, including a very frustrating phone call to apple support who of course will not acknowledge there is an issue.