A woman had bought two marmosets - a small long-tailed South American monkey - from a pet shop.
However, the pair then mated and soon she had six monkeys to care for.
The woman kept the monkeys for five years before contacting the RSPCA because she couldn't care for them.
RSPCA officers went to the home in February to catch and transport the primates.
They were taken to a vet surgery for check-ups and the males had vasectomies.
National exotics coordinator Inspector Kim Greaves said: "We were contacted by a woman who had bought two marmosets from a pet shop which soon became a family group of six; three females and three males.
"She'd had the monkeys for five years and approached us to ask for help because she was struggling to meet their needs."
The marmosets have now been moved to a private exotics specialist sanctuary in Cambridgeshire.
The charity is now calling for a ban on keeping primates as pets.
Kim said: "Now, the marmosets have a huge enclosure with the stimulation, space and enrichment they need to keep them happy.
"However, many of my colleagues have seen primates being kept alone in shocking conditions cooped up in tiny, filthy cages and fed fast food, fizzy drinks and even drugs.
"Often these primates will have behaviour problems and poor health due to inappropriate care."
SPCA Senior scientific manager, Dr Ros Clubb said: "We're delighted that a ban on keeping primates as pets is now in sight and we hope that the legislation will deliver an end to the keeping and trade of primates as pets.
"Primates are intelligent, sentient and highly social animals with complex needs that simply cannot be met in a domestic environment.
"Just like humans, primates can become depressed without adequate stimulation.
"They need a spacious and enriched environment that challenges their intelligent brains and allows for them to behave like primates should."