Peacock was born in Melbourne and attended Scotch College before studying law at the University of Melbourne. A former president of the Young Liberals, he was elected to Parliament at the age of 27, filling the blue-ribbon seat of Kooyong, vacated by Sir Robert Menzies. Peacock was appointed to cabinet in 1969 by John Gorton and later served under William McMahon and Malcolm Fraser. He held a variety of portfolios, most notably serving as Minister for Foreign Affairs from 1975 to 1980. He unsuccessfully challenged Fraser for the Liberal leadership in 1982, but was then elected as Fraser's successor following the party's defeat at the 1983 election.