Their report calls for a new rules to supervise sensitive research that involves humanising animals.
One area of concern is "Category Three" experiments which may raise "very strong ethical concerns" and should be banned.
An example given is the creation of primates with distinctly human characteristics, such as speech.
Exactly the same scenario is portrayed in the new movie Rise Of The Planet Of The Apes, in which scientists searching for an Alzheimer's cure create a new breed of ape with human-like intelligence.
The report also acknowledges the "Frankenstein fear" that humanising animals might lead to the creation of "monsters".
Currently research involving great apes, such as chimpanzees, is outlawed in the UK. But it continues in many other countries including the US, and British scientists are permitted to experiment on monkeys.
Professor Thomas Baldwin, a member of the Academy of Medical Sciences working group that produced the report, said the possibility of humanised apes should be taken seriously.
"The fear is that if you start putting very large numbers of human brain cells into the brains of primates suddenly you might transform the primate into something that has some of the capacities that we regard as distinctively human.. speech, or other ways of being able to manipulate or relate to us," he told a news briefing in London.
"These possibilities that are at the moment largely explored in fiction we need to start thinking about now."
Prof Baldwin, professor of philosophy at the University of York, recommended applying the "Great Ape Test". If modified monkeys began to acquire abilities similar to those of chimpanzees, it was time to "hold off".
"If it's heading in that direction, red lights start flashing," said Prof Baldwin. "You really do not want to go down that road."
In the US, scientists have already implanted human embryonic stem cells - which can develop into any part of the human body - into mouse embryos.
The mouse cells rapidly outgrew the human stem cells, so that only a tiny proportion of the embryos ended up "human".
Working group member Dr Robin Lovell-Badge, a leading geneticist from the Medical Research Council's National Institute for Medical Research, said this was not surprising given the differences between mice and humans.
But he added: "If you were to do that experiment with a non-human primate you can't predict the result.
"It could be that you get a low contribution (of human cells) or you can control the contribution and end up with an animal that ... wouldn't challenge, too much, public values. But on the other hand we can't predict that at all now.
"It's unpredictable and you could end up with an embryo that is too much human-like."
A public poll carried out for the report showed that most people accepted animals being modified with human cells or genes to support medical research. But there were real concerns both from members of the public and scientists about experiments involving the brain, fertility, and "uniquely human" features such as facial shape, skin texture or speech.
"We all laugh when we see cartoons of talking meerkats or cats with opposable thumbs," said Prof Lovell-Badge. "If we were actually doing that in the labs I don't think people would be so happy."
The report highlights a short story by Franz Kafka - appropriately entitled A Report To The Academy - about a circus ape which has learned to speak.
"It is not a comforting story and Kafka clearly writes to make one wonder what 'it might be like' for a chimpanzee to be in this situation," wrote the scientists. "So there is a 'Kafkaesque concern' which we need to take seriously, alongside what one might call the 'Frankenstein fear' that the medical research which creates 'humanised' animals is going to generate 'monsters'."
Currently all animal testing is regulated by the Home Office through the Animal Procedures Committee (APC), which provides advice and expert opinion.
The report calls for a national expert body run by the Home Office to provide specific advice on sensitive "animals-containing-human-material" (ACHM) research. In practice, this might involve widening the scope of the APC.
The working group also wanted to see a new system of categorising ACHM experiments. Category One would include uncontroversial work regulated the same way as any other animal research. Category Two would cover a "limited number" of procedures demanding "strong scientific justification" which would be subject to extra specialist scrutiny.
Category Three experiments would not be allowed because "they lack compelling scientific justification or raise very strong ethical concerns".
Prof Lovell-Badge said: "Scientists are very inquisitive beings. They like to do things. We haven't come across any scientists who want to go into Category Three, definitely, but there are those who want to do Category Two experiments."
ACHM research that has already been conducted includes the creation of mice with a gene linked to human speech.
The mice did not speak, but made vocal sounds that were different from those of "normal" animals, said the scientists.
Another experiment involved mice with "human" livers derived from human cells, goats with a human gene that produces a protein for treating blood clotting disorders, cancer research mice implanted with human tumours, and the "Down's mouse" used to investigate Down's syndrome that carries around 300 human genes.
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."
Lord Willis, chair of the Association of Medical Research Charities, said, "New techniques to incorporate human cells or genetic information into animal models have the potential to find solutions to conditions that are currently life-threatening or debilitating, and the Academy's proposals will give scientists that opportunity without compromising tough regulation."
Sir Paul Nurse, president of the Royal Society, said: "The Royal Society is supportive of the recommendations made in this report, especially the call for a national expert body to advise on ACHM.
"Proper scrutiny and regulation of this developing field now will ensure that society benefits from its advances fully."
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