Highmore was born on 14 February 1992 into a show business family. His mother, Sue Latimer, is a talent agent whose clients include actors Daniel Radcliffe and Imelda Staunton, and his father, Edward Highmore, is an actor. He has a younger brother named Albert ("Bertie"), born in 1995. Highmore's home is in Highgate, an area of North London.
Highmore was educated at a primary school in Hampstead Garden Suburb in Hampstead in North London, and at Highgate School, an independent school for boys in Highgate (also in North London), followed by Emmanuel College at the University of Cambridge, where he studied Spanish and Arabic.