iMessage on iMac Not Authorising

Good Evening,

Would appreciate your help gang, thanks in advance.

Since update to MAC OS Catalina - iMessage is no longer authorising.

I have followed the online support steps, updated (an already functional) Apple ID with a new password, cleared caches and re-installed Catalina (just in case).

Emails and details are recognised as correct...

I get the above message and "failure to authenticate"

Appreciate your time,

Keep Well