As someone who's worked on a major UK government website, I can tell you those badges have very specific meanings and a set of criteria attached to them.
Due to security reasons (that I don't necessarily agree with!) a lot of those sites will never leave Beta.
This is all public information which can be read at, https://www.gov.uk/service-manual/agile-delivery/how-the-beta-phase-works#moving-from-public-beta-into-live