In answer to Peter's original question, I think that this is a full list of Lennon/McCartney songs that were given to other artists (but I'm happy to be corrected). The dates are the initial release years by the artist concerned. I've not included songs such as 'I Call Your Name' or 'I Wanna Be Your Man' which were initially recorded by someone else, but later done by The Beatles themselves. Hope that this is of interest.

Ed

The Applejacks
Like Dreamers Do (1964)

Badfinger
Come and Get It (1969)

Chris Barber Band
Catcall (1967) Instrumental. This tune is known as 'Catswalk' in most Beatle biographies

Cilla Black
Love Of The Loved (1963)
It's For You (1964)
Step Inside Love (1968)

Black Dyke Mills Band
Thingumybob (1968) Instrumental

The Fourmost
Hello Little Girl (1963)
I'm In Love (1963)

Mary Hopkin
Goodbye (1969)

Billy J Kramer and the Dakotas
I'll Be On My Way (1963)
Bad To Me (1963)
I'll Keep You Satisfied (1963)
From A Window (1964)

Peter and Gordon
World Without Love (1964)
Nobody I Know (1964)
I Don't Want To See You Again (1964)
Woman (1966)

PJ Proby
That Means A Lot (1965)

Tommy Quickly
Tip Of My Tongue (1963)

The Strangers with Mike Shannon
One And One Is Two (1964)