How to change billing address for iCloud subscription

The billing address and the shipping address can be edited by clicking on Payment Methods (in the list at the left) of the Apple ID site. After clicking on Payment Methods you will see over on the right ‘Manage Payment Methods’. Click on this to bring up a panel with your billing and shipping details. Change as appropriate.

The contact details are also available in the Apple Store, where they are needed for purchases.

You can access your Apple Store account using the same Apple ID credentials: Apple Store Online

Go to the Apple Store then at the foot of that page is a link to account sign in. Click that, sign in, and you will find the Account Settings at the lower part of the screen. The Shipping Address, Billing Contact, and Billing Address - as well as your payment method - can all be edited here.

Update your billing details in your Apple ID account by signing in here.

This doesn't work; my billing address (incorrect) is grayed out, while the shipping address (which is correct) is editable.

If it isn't working as expected your next step should be to contact Apple Support. Click on 'Show All' and select Apple ID.