I'm sure HMRC do run their own datacentre kit
But for any large organisation, a hybrid of physical data centre kit and cloud provisioned services will give the most flexibility and resilience.
HMRC see a peak every year when personal tax submissions are due. Keeping a number of extra servers on standby for 11 months for a 1 month peak would be stupid. Better instead to (automatically) spin up a number of cloud hosted servers for the short busy period. The extra capacity can be (automatically) switched off and forgotten about as soon as they are no longer needed. On premise kit can deal with the load for the rest of the year.