Users around the world have been experiencing problems with iMessage not working since upgrading to iOS 7. Apple has acknowledged the issue but has not provided a fix. Apple News has confirmed that the steps below do resolve the issue however we cannot confirm it the issue will start again. It the problem does start again you can follow these steps again and it will resolve the issue.
- Turn iMessage off in Settings > Messages.
- Turn iMessage back on.
- Turn your device off and back on again.
There is another solution floating around on the internet but doesn't recommend you do it because you will lose all Wifi passwords.