How to fix the 'Not Delivered' SMS issue on iPhone?

Trying to reply to an SMS text message results in the reply being 'not delivered' and an an exclamation mark in a circle, both shown in red. Tapping the exclamation mark opens a choice option at the base of the screen that asks 'Try Again'. This results in another 'Not Delivered' message.

I have checked the messaging app and all settings appear to be in line with all the 'help' published when investigating this problem. I have refreshed the messaging App, shut down the phone and restarted, but none of these actions have helped.

SMS is such a basic phone operation, please advise a solution please!!

[Re-Titled by Moderator]