Don't you have to have a permit to keep them though? From what I've seen from Monkey World's work is that they aren't all that good at inspecting the housing though. I think it depends on the borough council, I think they are the people who warrant the permits.
The only 'permit' required in the UK for any animal is a DWA licence. Only animals considered dangerous require this, so big cats, big primates, venomous snakes, etc. Marmosets, small primates, small cats, those kind of things, they're not on the list, so anyone can have one if they buy one.
Monkey worlds take has two issues, firstly, they take animals from people who can't cope, so yes, they show people who are clueless and keeping animals badly, quite few considering the huge amount kept here.
Secondly they are anti primate captivity, this has mellowed in recent years, but originally they were reluctant to let animals go to other zoos, and would never approve of a private individual keeping primates, no matter how well. Due to this they are much more eager to show their rescues from private homes with dreadful accommodation than those who came from better homes but due to a deceased owner for example.