I had a similar problem on my iPhone 5 and iPad 2 with iOS 7. For me not only did iCloud mail not push, but neither did other iCloud services such as Reminders and Calendar.
I had the advantage of having a work iPhone 4S and iPad 3 so I was able to try various things with 4 devices to see if I could figure out my problem. After setting everything to my personal iCloud account the only thing that pushed correctly was the iPhone 4S. I tried everything such as deleting and reentering my iCloud settings, changing other settings to see what might happen, and totally resetting my devices and restoring them from their backups. Nothing worked.
I finally decided I had to try the nuclear option and totally reset my devices and not restore them from a backup. That's right, I set each one up as a new device. Of course, I lost a couple of game saves and had to reenter a bunch of settings but each device worked correctly after that. All 4 devices now work.
I hate to be the bearer of bad news here. I hope Apple or someone comes up with a better solution than I did.