Has anyone successfully gotten a credit balance refund from Amex UK?

I keep going round in circles with receiving letters asking for documentation relating to the account that the refund needs to go in to, and I keep providing this but after 2-3 weeks I get the same template coming through the post again. This has been happening for three months.

When I call Amex, I get told that there’s no update from the “back office team” aside from they have sent me a letter requesting details of the account that the refund is to be made to. Apparently it’s not possible to speak anyone from this back office team either, you have to wait for them to send a letter in the post.

What is the way to resolve this? I’d prefer to not close my account, but it’s getting to the point where I’m not sure what else is left.