Hi Robert,
You have two options:
1 - host your own Portal, AGS/SDE in Amazon, Azure or Rackspace. That is not that simple or cheap to do, since you need to take in consideration high availability and disaster recovery, license costs, infrastructure costs etc.
2- host your map services or web applications in one of the UK companies offering this service. The map services can be used elsewhere (desktop, AGOL, etc). All support to the service and data management is done locally. MSaaS - map service as a service