I would not call the GDS design "brutalist". As the linked article says, brutalism is about "raw [content/architecture], true to its construction". In other words, it's an aesthetic movement that pretends it's not about aesthetics.

The GDS design guides are not rooted in aesthetics, they're truly rooted in practicality. Their goal is for the site to be navigable and understandable by as close to 100% of the UK population as they can get. That has to include people with old or unusual devices, people with disabilities, people on slow connections, and so on. It's all about the user.

Actually-existing brutalist buildings are not like this. The architects put aesthetic sensibilities first, usability second, while fraudulently claiming they were doing the opposite[1]. When people complained about how unpleasant it was to live in them, they did the "you're holding it wrong" dodge, and said the users (i.e. inhabitants) were to blame.

[1] For example, they would put in industrial-looking concrete greebles on the sides of buildings, making them look like they served a structural purpose, but actually they didn't. It was purely decorative, but ugly decoration that only appealed to other brutalist architects, meant to trick people into thinking it was some "raw" construction element sticking out.

EDIT lol the stained concrete appreciation society have arrived; but no amount of downvotes will make anyone want to live in coventry