On the basis of his youthful looks, strong stage presence, and soulful voice, Island Records signed Palmer to a solo deal. His first solo album Sneakin' Sally Through the Alley recorded in New Orleans, Louisiana in 1974, was heavily influenced by the music of Little Feat and the funk fusion of The Meters who acted as backing band along with producer/guitarist Lowell George of Little Feat. His first single was a cover of Little Feat's "Sailin' Shoes." Although moderately successful in the UK, both the album and single reached the Top 100 in the US. Notably, "Sailin' Shoes" (the album's first track), Palmer's own "Hey Julia" and the Allen Toussaint-penned title track carry virtually the same rhythm, and are packaged on the CD as a "trilogy" without a pause between them.
Subsequently relocating from London to New York City with his wife, Palmer released Pressure Drop in 1975 (featuring famed Motown bassist James Jamerson). An album infused with his interests in reggae and rock music, it was noted for its cover art of a nude girl on a balcony rather than any commercially successful songs. (The lead single "Give Me An Inch" did win critical plaudits for Palmer's note-perfect delivery and its chord changes, which surprised George during the recording process.) He toured with Little Feat to promote that album.
However, with the failure of the follow-up Some People Can Do What They Like , Palmer decided to move to the Bahamas; after that, his "expatriate lifestyle" was likely to receive more coverage than his music in British newspapers.
In 1978, he released Double Fun, a collection of Caribbean-influenced rock, including a down-tempo and syncopated cover of "You Really Got Me". The album reached the Top 50 on the US Billboard charts and scored a Top 20 single with the Andy Fraser-penned "Every Kinda People". With its blend of Caribbean steel pan, violins and moving lyrics, "Every Kinda People". has become one of Palmer's best-loved songs, covered multiple times by other artists (including Chaka Demus and Pliers, Randy Crawford and Amy Grant) and cited by music fans and spiritual groups for its positive message.
Palmer's next album was an artistic departure, concentrating on a rockier direction. 1979's Secrets produced his second Top 20 single with Moon Martin's "Bad Case of Loving You (Doctor, Doctor)", which like "Every Kinda People" became one of his signature tunes.
The 1980s saw Palmer find an increasing amount of commercial success. The album Clues, produced by Palmer and featuring Chris Frantz and Gary Numan, generated hits on both sides of the Atlantic, first with the radio-friendly single "Johnny and Mary" and then "Looking for Clues". Catchy music videos matching the synth pop stylings of New Wave gave him much needed exposure to a younger audience. The success was repeated with the 1982 EP release of Some Guys Have All the Luck.
1983 saw Palmer blend techno beats, early sampling and more of the island music of his adopted Bahamas (including steel pan) into the adventurous album Pride. Though the album wasn't the smash Clues was, it did feature standout tracks in the title song and Palmer's cover of The System's "You Are In My System", with The System's David Frank contributing keyboard tracks to the latter song.
"You Are In My System" was an example of Palmer's passion for R&B covers. He jammed the song onto the Pride album after the other tracks were finished. Hearing the track in a Paris club, Palmer rushed back to his Bahamas hometown, where the reconvened band (co-composer Frank included) put together the number. Esquire magazine recounted the tale of the last-minute addition later that year. Palmer did the same in liner notes for his 1992 Addictions Volume 2 CD, which included his re-voiced version of "You Are In My System."