As another British person I'm unconvinced that "British interests" include the interests of most British voters.

Historically we've seen the British state infiltrate and influence organisations that it considers hostile to it.

https://www.theguardian.com/uk-news/ng-interactive/2018/oct/...

What stands out is the trivial nature of most of these groups, which surely fall squarely within a general democratic right to assemble and protest.

What also stands out is that right-wing groups don't seem to have had anything like the same level of oversight.

So if - hypothetically - the military and/or GCHQ ran a campaign to influence a British election, or a public referendum, would that align with "British interests" or not?

This isn't a hypothetical. It's obvious from the comment sites of most newspapers and also from posts on FB interest groups that industrial-level opinion-shaping is being attempted.

If it's originating from hostile foreign powers, the UK's cyber response seems inexplicably ineffectual. If it's originating from closer to the home, that's clearly a non-trivial problem for our "general values."