In a decision that has been labelled "grotesque" by animal rights campaigners, Prescott said that the proposed research centre on Huntingdon Road in Cambridge is of national importance and added that a refusal could jeopardise the future of neurological research in the UK.
The laboratory, proposed by Cambridge University, will carry out research aimed at tackling neurological diseases such as Alzheimer's and Parkinson's.
But its intended use of primates for testing has attracted vehement opposition from animal rights campaigners.
South Cambridgeshire District Council refused permission for the proposal two years ago, arguing that campaigners' demonstrations against the facility could result in road blockages and a danger to public safety.
But Prescott ruled that the scheme would be "a vital contribution to the government's aim to promote an internationally competitive knowledge economy in the UK that will generate wealth and deliver health and other benefits". A refusal would risk losing the opportunity to strengthen both Cambridge's and the UK's role in leading-edge research, he argued.
Andrew Tyler, director of campaign group Animal Aid, said that the decision is "grotesque and astounding given that the government official who presided over the public inquiry was clear that permission should not be granted".
But Tony Minson, pro-vice-chancellor of Cambridge University, welcomed the decision. "It is reassuring that the government is sending this message of support for neuroscience in the UK," he said. "The university remains convinced of the national importance of this research. Neurological diseases have a huge worldwide impact and combating these devastating conditions is a major scientific priority."