Apple ID - country code not valid?

I am trying to connect my phone number to my Apple ID, and I can't. I keep getting the prompt "please enter a valid country code" – across all my devices.

I have an Icelandic phone number and the country code for Iceland even gets automatically selected on my iPhone. It IS a valid country code because I know loads of people who have Icelandic phone numbers linked to their Apple IDs.

I suspect this is an issue because my OLD phone number is a UK number, which obviously has a different country code. Has anyone else had this issue? Is it linked to switching between different country codes? What can I do?