If existing companies utilize cloud providers and CDNs rather than investing in their own in-house infra, doesn’t that signal to you that perhaps your analysis of the situation is flawed?

It’s possible the government is a big enough customer that they could get the necessary economy of scale to make it cost effective, but it also means that they’re going to need to develop a bespoke solution that all government services build on which itself is an expensive endeavor (and politically a liability since such a project can fail to deliver and just balloon in cost).

Let's imagine that I had to make a website that could host a million concurrent users once per year. What do you think is cheaper, me acquiring all of the hardware to scale to a million users and then leaving it idle 99.9% of the time, or outsource handling that peak traffic to someone who's already operating at the scale for it?

The UK government does not remotely need the same year-round capacity as a top-tier CDN.