Peacocke was born in Pittsburgh, Pennsylvania, and raised in Canada, and holds citizenship of both the United States and Canada. He graduated from Université de Caen, France, then attended Yale University, where he graduated magna cum laude in 1983. He later studied at New York University Tisch School of the Arts between 1983 and 1984. Peacocke married British citizen Amanda Pieris in the 2010s. Peacocke is well-known in the Canadian television industry, and has directed episodes of Madison, Cold Squad, Blue Murder, Traders and Made in Canada.

He has won two Canadian Comedy Awards for Best Direction of a television series (for Made in Canada in 2002 and Rent-a-Goalie in 2007) and a Gemini Award for Best Direction in a Comedy Program - Rent-a-Goalie in 2008).

He has directed more than 140 episodes of over twenty-five different television series, including Rookie Blue, Heartland, The Border, M.V.P. (which he also produced), Rent-a-Goalie, Show Me Yours, The Eleventh Hour, Blue Murder (on which he also served as creative consultant), Mutant X, Made in Canada, Cold Squad, Amazon, Traders, North of 60, The Rez, Black Harbour, The Crow: Stairway to Heaven, Jake and the Kid, Madison, Beast Wars: Transformers, The Odyssey, and Schitt's Creek. He also directed the four-hour television mini-series, Canada Russia '72, for which he received a Best Director Gemini Award nomination.

He has appeared as an actor numerous times, in episodes of Rent-a-Goalie, Traders, Madison, and Canada Russia '72, in which he played the captain of the Soviet hockey team, Victor Kuzkin.