Born in Camden Town, London; his father was Seafield Head, the founder of Verity Films, and his mother was the actress Helen Shingler. His older brother is actor and singer, Murray Head. Anthony was educated at the London Academy of Music and Dramatic Art (LAMDA). His first role was in the musical Godspell; this led to roles in television on both BBC and ITV and then a series of twelve coffee commercials for Nescafé Gold Blend, which was what brought him fame. Success on the stage and a number of brief appearances on American TV such as the short-lived VR-5 led to accepting the role of Rupert Giles in Buffy in 1997.
In 2002, he appeared in the British television series Manchild, concerning four fifty-something men who spend all of their time talking about sex. He also released an album of songs with musician George Sarah entitled Music for Elevators and guest starred in a series of Doctor Who audio adventures.
There is persistent talk of Head starring in a Buffy spin-off series for the BBC entitled Ripper, but so far nothing has come of this.