Better regulation is needed to govern rapidly expanding research in animals containing human tissue or genes, the Academy of Medical Sciences says.
It said such studies were necessary for medical research, but that new ethical issues could emerge and called for a national body of experts.
It said "category three" experiments on monkey brains, resulting in "human-like" behaviour, should be banned.
The government said it would consider the recommendations.
Dr Robin Lovell-Badge, from the National Institute for Medical Research, said: "Everyone laughs at talking meerkats and cats with opposable thumbs, but if we were actually doing that in the labs I don't think people would be so happy."
Introducing human material into animals has furthered medical research.
Putting human breast tumour cells into mice has allowed researchers to test cancer drugs on human tissue.
Stroke damaged mice showed some recovery when their brains were injected with human neural stem cells, which has led to human clinical trials.
Mice with Down's syndrome have had a whole human chromosome added to their genome to help researchers learn more about the condition.
Professor Christopher Shaw, from King's College London and one of the report's authors, said animals with human material were "hugely important. Is [the field] going to shrink and go away? No. I'm confident it will lead to new treatments."
The academy report said it was anticipating "a major increase in the use of these techniques".
However it raised concerns that some cases would fall through gaps in the regulation.
The authors said that, for example, experiments on an embryo which contained predominantly human material would be controlled by the Human Fertilisation and Embryology Authority and the embryo would not progress beyond 14 days. For embryos which are mostly animal, but contained some human material, they said there was "no regulation at all".
Animal research is regulated by the Home Office's animal procedures committee.
Professor Martin Bobrow, chair of the Academy of Medical Sciences, said: "Our report recommends that the Home Office puts in place a national expert body, within the existing stringent system of animal research regulation, to provide specific advice on sensitive types of 'animals containing human material' research."
The academy recommended three classifications for research on animals containing human material.
Most would be "category one" and have no more restrictions than any other study on animals.
Category two experiments could be allowed but "would require strong scientific justification". The report suggested this would include adding genes to non-human primates and significant changes to an animal to make it "more human-like".
Category three experiments would not be allowed, such as letting any mixed embryo develop past 14 days or breeding animals with human influenced sperm or egg cells and modifying non-human primates to create human-like awareness or behaviour.
Professor Bobrow was keen to stress that "nobody has done any of these things", but the Academy of Medical Sciences said it wanted guidelines in place rather than waiting until the horse had bolted.
Home Office Minister Lynne Featherstone said: "We welcome the valuable contribution of this study to the understanding of the complex ethical, scientific and animal welfare issues involved in this area of research.
"We will consider the recommendations carefully."