How do you disable the iOS Storage full alert?
Apple do not provide any way to stop what it perceives as important alerts.

That said, for those with jailbroken phones, popup blocker provides the required functionality

Edit: the original question is answered in the most part, but i think the real question should be 'Why am i getting the ios Stoage almost full" alert.

this is either a bug, or you've got a lot of mail stored on the phone...

There appears to be a few users with the same issue over on the Apple support forums here