I find there are three types of private primate keepers in the UK and believe me not all are appalling, some are even better than zoos!
1. The worst kind where single marmosets are kept in parrot cages, generally where people just "wanted a monkey" as a pet. These are usually fed a bad diet and sadly will not live as a primate should live.
2. Private keepers who are quite open about their primate collections and generally keep them in large outdoor enclosures in mixed family groups, giving them very good diets and making sure the offspring are at least 18 months old before they are moved on to create other groups.
These are generally the more common marmoset/tamarin species and squirrel monkeys.
These are not kept alone in an indoor pet setting and are very well cared for.
3. Very private private keepers who keep primates in much the same way as above but they generally keep much more unusual species such as capuchins, rarer tamarin species, lemurs, macaques etc.
Some of these keepers keep their animals in very large enclosures even letting them free range in open top enclosures much as you would see in a zoo.
1's Should be the group who are prosecuted and dettered from keeping primates but 2's And 3's Are the groups who shouldn't be lumped with 1's. Many work alongside zoos and even have studbook animals.