Q: I received an email saying my icloud storage is full so I will not receive any more email, yet I still have 12G of storage left. Today I have received no email;

People keep getting these false alarm emails but it doesn't usually have any effect on the account. Have you checked by sending yourself a message? If you do that and it doesn't arrive, does it get bounced back with an 'account over limit' message? If it doesn't arrive but you get no bounce it might have got stuck - it's not unknown for emails to get held up for some hours, and not just with Apple.

If messages really are being blocked you will probably have to contact Support.

To contact  iCloud Support: if you currently happen to have AppleCare, either because you recently bought Apple hardware or have paid to extend the inititial period, you can contact them here:

http://www.apple.com/support/icloud/contact/

You will need the serial number of the covered hardware.

If you are not covered by AppleCare, then - in common with other free email services - there is no free support and you may be asked to pay a fee. You should be able to argue that they are causing this problem and therefore you shouldn't be charged - but do make sure you have a case first.

Are you sure it's icloud storage that is full and not storage on your device?

Go to Settings>iCloud>Storage & Backups>Manage Storage; there, tap the device you need info on and the resulting screen lists Backup Options with which apps store data on iCloud as well.