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); "It Makes No Difference" (Joe Dolan); "Something Tells Me Something's Gonna Happen Tonight" (Cilla Black); "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); "Melting Pot", "Good Morning Freedom" (Blue Mink); "Green Grass" (Gary Lewis); and "Something's Gotten Hold of My Heart" (Gene Pitney). They also wrote "High And Dry" (Cliff Richard), which was the runner-up for the UK Eurovision Song Contest entry in 1968.
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. The following year Greenaway teamed up for a while with singer Tony Burrows to form Pipkins, a duo who had a Top 10 novelty hit in 1970 with "Gimme Dat Ding".
The New Seekers' "I'd Like to Teach the World to Sing" began life as a Cook-Greenaway collaboration called "True Love and Apple Pie", recorded by Susan Shirley. The song was then rewritten by Cook, Greenaway, Coca-Cola account executive Bill Backer, and Billy Davis, and recorded as a Coca-Cola radio commercial, with the lyric "I'd like to buy the world a Coke and keep it company." First aired on American radio in 1970, it was also used as a TV commercial a year later, sparking public demand for its release as a single. Reworked, again, to remove the references to the brand name, the single climbed to UK #1 and U.S. #7 in 1972.
After Cook moved to the U.S. in 1975, Greenaway worked with other partners, notably Geoff Stephens, both being jointly responsible for Crystal Gayle’s 1980 No. 1 country song, "It’s Like We Never Said Goodbye".
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. He also wrote advertising jingles for Allied Carpets, ASDA and British Gas.