I can't access UK legislation easily from here. However, it seems to me that this should be a straightforward Companies Act 1985 and Companies Regulation question. I suggest you look at those pieces of legislation in relation to companies limited by guarantee as a starting point. What are the various provisions re: memoranda/articles of association and how do they limit who can/cannot vote at an AGM? Are there any different CA85 provisions for a company limited by guarantee?
Avoid just sticking a couple of search terms into Lexis. With respect, that's the lazy approach. Try a couple of company law texts as a starting point. Then move onto the legislation itself. Otherwise, Halsburys will give you a good overview.