Peek was born in Panama City, Florida on November 1, 1950 while his father was in the U.S. Air Force.
When Peek was a young boy, he suffered from rheumatoid arthritis and had to be hospitalized for weeks 100 miles (160 km) away from the family home; his parents could only visit occasionally. Peek remembered this experience when, about a year before he died, he decided to dispose of five of his vintage guitars. Because the Ronald McDonald Houses exist to provide housing for families of hospitalized children close to hospitals around the United States and the world, Peek donated these five guitars to the San Diego house, which were subsequently sold to a collector, resulting in a $50,000 donation.
Peek moved to England in 1963 with his family when his father was assigned to a base in London, meeting Dewey Bunnell and Gerry Beckley at London Central High School.
Beginning in 1963, Peek was educated at London Central Elementary High School at Bushey Hall in North London. In 1973 he married Catherine Maberry, with whom he would write a number of songs, including "Lonely People". He published an autobiography entitled An American Band, based on America's most successful period, and his own spiritual journey.