I'm pretty sure John Lennon played the banjo on All You Need is Love. Here's the personnel:
John Lennon: vocals, harpsichord, banjo
Paul McCartney: vocals, bass, double bass
George Harrison: vocals, guitar, violin
Ringo Starr: drums
George Martin: piano
Sidney Sax, Patrick Halling, Eric Bowie, John Ronayne: violin
Lionel Ross, Jack Holmes: cello
Rex Morris, Don Honeywill: tenor saxophone
Stanley Woods, David Mason: trumpet
Evan Watkins, Harry Spain: trombone
Jack Emblow: accordion
Mick Jagger, Keith Richards, Marianne Faithfull, Jane Asher, Mike McCartney, Pattie Harrison, Eric Clapton, Graham Nash, Keith Moon, Hunter Davies, Gary Leeds and more: chorus
Mike Vickers: conductor
(The Beatles Bible)
Welcome back, Daniel. It's good to see you again.