 Fisher was an undergraduate student at Trinity Hall, Cambridge where he read Natural Sciences.He was a postgraduate student at St. Catherine's College, Oxford where he was awarded a Doctor of Philosophy degree from the University of Oxford in 1995 for research on positional cloning of the gene responsible for Dent's disease supervised by 

Following his DPhil, he was a postdoctoral researcher in Anthony Monaco's laboratory at the Wellcome Trust Centre for Human Genetics in Oxford.Fisher is the co-discoverer of FOXP2, the first gene to be implicated in a human speech and language disorder.