There is no justification in a country this size for them to be traveling by air at all unless it's an emergency where they're needed somewhere absolutely ASAP, or they need to travel directly from one end of the country to the other, which is almost never.
Just one more way in which those in power separate themselves from those they rule over.
I mean, that’s…the next model of the same helicopter. Is that actually less-expensive?
I would guess the government doesn't need to profit from buying flights from itself. A private company certainly isn't going to provide service without a percentage of profit on top charged to the government.
A "benefit" of using RAF helos is it the flight hours. Pilots typically need a certain number of flight hours every month to maintain their certs, so they'll likely be flying anyways. Having them fly senior ministers around instead of other training flights technically is free, as the flights were going to happen anyways.