His compositions have included "You've Got Your Troubles" and the transatlantic million-selling songs "I'd Like to Teach the World to Sing (in Perfect Harmony)"[2] and "Long Cool Woman in a Black Dress".

Their first single "Laughing Fit To Cry" did not chart, but they scored hits in 1966 with their cover version of the Beatles' "Michelle" and their own "Lovers of the World Unite".

Their hits as writers for other acts, sometimes with other collaborators, include: "Home Lovin' Man" (Andy Williams); "Blame It on the Pony Express" (Johnny Johnson and the Bandwagon); "Hallejuah" (Deep Purple); "Doctor's Orders" (Sunny (UK) and Carol Douglas (US)); "It Makes No Difference" (Joe Dolan); "Something Tells Me (Something's Gonna Happen Tonight)" (Cilla Black (UK)[5] and Bobbi Martin (US));[10] "I've Got You On My Mind", "When You Are a King", "My Baby Loves Lovin'" (White Plains); "Long Cool Woman in a Black Dress", "Gasoline Alley Bred", (The Hollies); "You've Got Your Troubles", "Freedom Come, Freedom Go" (The Fortunes); "Banner Man", "Melting Pot", "Good Morning Freedom" (Blue Mink); "Green Grass" (Gary Lewis & the Playboys); "New Orleans" (Harley Quinne);[11] "A Way of Life" (The Family Dogg) and "Something's Gotten Hold of My Heart" (Gene Pitney).

[12] The New Seekers' "I'd Like to Teach the World to Sing (in Perfect Harmony)" began life as a Cook–Greenaway collaboration called "True Love and Apple Pie", recorded by Susan Shirley.

[2] When Blue Mink were formed in 1969, Greenaway was asked to be lead vocalist alongside Madeline Bell; he declined the offer and recommended Cook, who accepted.

[14] The following year Greenaway teamed up for a while with singer and former Kestrels band-mate Tony Burrows to form the Pipkins, a duo who had a Top 10 novelty hit in 1970 with "Gimme Dat Ding".

[15] The same year, he was briefly a member of Brotherhood of Man, also featuring Burrows as lead singer, who scored a UK and US top 20 hit with "United We Stand".

[7][17] Greenaway took an increasing role in business administration, becoming Chairman of the Performing Right Society in 1983 and, in 1995, taking charge of the European ASCAP office.