Lambeth is apparently contemplating a staff mutual for its libraries. Working out the detail of such arrangements is complicated, and there would be a big risk to the staff if it failed.
Brent has yet to reveal what the rather cryptic mention of libraries in the last budget process actually meant. I think a user based Co-operative might be worth considering. Brent libraries have a ready made pool of potential co-operators in everyone who has a library card, and they can be proven to have an active relationship with their libraries through the records of book borrowing and computer use. Such an arrangement, I think, would be able to exploit the tax avoidance device of not paying business rates which is the cash saving that Brent identified in the budget as (apparently) the main advantage of the proposal.
Whether this cash saving is worth having I think is rather questionable. As business rates are going to be localised, at least if George Osborne gets his way, any rates not collected on Council buildings simply reduce Council revenue, so it isn't really a saving at all. The saving, however, remains a line in the budget so I take it that Brent libraries will have to find the money by some other means. that again underlines the importance of Brent libraries putting together a proper library strategy now that the Libraries Transformation Project has been implemented.