I think that this is probably genuine, but it's exactly the sort of thing that arouses my suspicions ...
I've just had an email from Three (of which I am a customer), telling me that they have updated their system and that I need to re-register my email and password to be able to access my account. But the thing is, neither the email, nor the link that it suggests I click on, come from three.co.uk - instead they refer to three-email.co.uk. A Google search on that doesn't come up with concerns, but it is the sort of address that a spoofer might use.
When I do re-register, rather than use the link, I will go in via three.co.uk and see whether that re-directs me.
Three is migrating all users to a new billing system and it will require re-logging in, so they have been informing customers before the change takes place (it's possible for there to be some downtime). However you won't need to do anything. I guess scammers have seen an opportunity to get in on something that a search might - on the surface - confirm there's a change and make their request more plausible.