As far as I can tell, CUK have actual local clubs on the ground.
Do they though? There are local CTC groups that are affiliated to the national organisation but the central government of CUK seems to be quite a distinct body, mainly focused on national-level campaigning, while the local groups get on with the business of organising rides.
In this respect, the relationship seems very similar to that between clubs and BC.
It's quite hard to make direct comparisons, both have affiliated clubs, in both cases those clubs can insist of joining the national organisation to be a club member, Cycling UK has a specific membership category for these, I don't think British Cycling do. British Cycling seem to exert more influence over their affiliated clubs and possibly offer them more in return. Cycling UK's affiliated clubs have in many cases affiliated just for the insurance and have no interest beyond that, likewise the affiliated members.
What Cycling UK has that British Cycling doesn't is Member Groups and these are a part of Cycling UK. They're left to largely organise themselves though they are obliged to follow certain policies. Their finances are included in CTC's accounts, they receive funding and other benefits. You can't join one of these Member Groups, everything they do is open to all Cycling UK members, from the rides to the AGMs.
DuncanM is right in this, what he doesn't do is put it in proportion, there's not many of these groups (140?) and the percentage of members who are actively involved with them is small. There's been a feeling (Mine anyway) that the national organisation had lost interest in these groups, but that seems to be changing.