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).