In 2003, Hunt was made an honorary Fellow of the Royal Society of Edinburgh (HonFRSE). In 2006, he was awarded the Royal Society's Royal Medal, two of which are presented annually for "the most important contributions to the advancement of natural knowledge", in his case for "discovering a key aspect of cell cycle control, the protein cyclin which is a component of cyclin dependent kinases, demonstrating his ability to grasp the significance of the result outside his immediate sphere of interest".