Can't join iCloud: "You can’t sign in because your account was disabled for security reasons."

I have a new iPhone and have just upgraded my Macbook Pro to Yosemite in order to share contacts and appointments, etc.

I go to start up iCloud for the first time; I get this message:

"You can’t sign in because your account was disabled for security reasons."

It gives me the option to reset my Apple ID - so I do.

I am emailed a link which allows me to enter a brand new password.

I do this on my computer and on my iPhone.

I return to Preferences to set up iCloud; I get the same message:

"You can’t sign in because your account was disabled for security reasons."

This is circular and is clearly a bug.

What do I do about it?