Or, informal term for a group of corporate law firms based in the UK. It wasn't clear to me what the article was actually about until the very end, not sure why didn't feel like spending at least one sentence making it clear up front who they're talking about.
I also assumed they were talking about a magic circle law firm. It's compounded by the fact that this kind of story is something you wouldn't be surprised hearing about a law firm in the old days (though hopefully not as late as 1991).