iMessage failed activation

The troubleshooting methods are available in the support document that you linked to the forum with. https://support.apple.com/en-us/HT201422

If you are having difficulty accessing the server, are you connected to the internet? Are you using a supported carrier for the iPhone? Activation requires sending and receiving a hidden SMS to the iMessage server in the UK. Unsupported carriers do not allow these, and some other carriers block international SMS. Do you have an SMS plan on your phone?

I spent all afternoon trying to resolve my issue with iMessage. Finally I read an article that said...switch your iCloud on or off. Reverse of your current setting. As crazy as it sounds, it fixed my problem.