I have the same issue on a refurb Iphone 6s. Sim was transferred from an Iphone 5C (which worked). Following the Apple suport pages has not resolved it. I have found that if you disconnect from a wi-fi route and try and use the cellular data to register iMessage or Facetime, it reports that the mobile data is not available... which has far as I can tell it is wrong ( as it browses web and receives emails. All the mobile data options are turned on against all the apps.
I also have a work Vodaphone sim, put that in and it initialised in seconds. Back with the VM sim and it fails.
I have had several "chats" with VM customer service and am now being sent out a new sim:- will let you know.
I swap my sim few days ago and now my iMessages are not activating. I tried everything possible. I swap the sim one more time. 2 sims from past one week. Called Apple Support as well. Still not working. Is there anyone else facing the same issue ?
Virgin Technical Support Team - Do you have any solution ? Can someone help ?