Change Business Address – simple, most effective way?

Normally with any other website, this would be simple. But getting set up on Amazon was a pain to begin with so I assume changing my business address is going to be an issue to. I have plenty of proof of my new address but was curious if this is a complicated process? If I would be taken off Amazon whilst they approve my new address etc.?

Do they need much info? I’ve literally just moved addresses, however I haven’t updated my business registration with HMRC yet (I’m sole trader)