Two of the earliest Lennon/McCartney songs are “One After 909” and “Hello Little Girl”, both written primarily by John Lennon; Wikipedia says that they date from 1957.  “One After 909” was included on the Beatles’ very last album, Let it Be and was also performed during the famous rooftop concert that is included in the film, Let it Be.  

“Hello Little Girl” was included on the Decca Records audition tape; there is also a home demo recording of the song that features Stuart Sutcliffe on bass guitar, which is currently available only on bootleg albums.  A version of “Hello Little Girl” by the Beatles is included on Anthology 1. 

Like “I Wanna be Your Man”, which was first recorded by the Rolling Stones, “Hello Little Girl” was one of the songs that they gave to others to record.  A little known Liverpool band (at least in this country) called the Fourmost first recorded “Hello Little Girl” in 1963 and made it to #9 on the British charts; Gerry and the Pacemakers also recorded the song in this time period.  

(June 2015)