The Social Enterprise model is well established. It is what it is, a non-profit making venture with social interest at its heart (supposedly). There are several legal models that can be applied to Social Enterprises, 'Community Interest Company' being one of the most recent.
As you say, it's really just variations on the co-operative theme.
Incidentally, it's not wise to assume that all NFPs are 'noble'. I saw it happen routinely in the States (where, in some areas, there are almost more NFPs than regular businesses) and I know people who've done it here; it can often be used very cynically whilst, ironically, outwardly maintaining the impression of being caring, altruistic and unconcerned about money. I know some people who've become very rich thanks to their 'Not for Profit' companies.