The son of actors Nigel Davenport and Maria Aitken, he spent much of his youth on a farm run by his parents. After their separation, Davenport was sent to boarding school. Although he tried acting in his first year at college, he had no intention of following in his folks' stead but fate intervened. His mother had appeared as John Cleese's wife in "A Fish Called Wanda" (1988) and she suggested her son contact Cleese who was making a sort of reunion film, "Fierce Creatures" (lensed 1995; released 1997). Davenport, who had majored in film studies, inquired after a production job. Cleese, however, forwarded the letter to the film's casting agent who hired Davenport for the small role of a student zookeeper.

Now intrigued by acting, Davenport went through a rigorous audition process to land his star-making role as Miles. Once he became a known quantity, he began landing parts in other British productions, like playing Malcolm in a 1998 TV version of "Macbeth". Moving away from his image as a bounder, Davenport played the first of several police detective roles in another cult British series, "Ultraviolet" (1998). Often referred to a low-budget take on the popular US series "The X-Files", the actor was cast as a leather jacket-wearing cop whose duty was to track down vampires. As it happened the role was a warm-up for his feature turn as a detective investigating murders committed by a vampire (Jude Law) in "The Wisdom of Crocodiles" (1998; released in the USA in 2000). He and Law were both also featured as jet set chums who have ties to Matt Damon's title character in the high profile Anthony Minghella drama "The Talented Mr. Ripley" (1999). As the homosexual musician Peter Smith-Kingsley, Davenport offered a memorable supporting turn and his scenes with Damon crackled. While he awaited that next big screen role, the actor returned to British TV to co-star with Iain Glen in the period thriller "The Wyvern Mystery" (BBC, 2000). He returned to series work later that year acting opposite Gina Bellman in the sitcom "Coupling".