This Lennon/McCartney song was also given away to Billy J Kramer & The Dakotas. It was tailored to their colleagues who were also managed by NEMS' Brian Epstein. Also this one was produced by George Martin. BBC recorded a Beatles version of "I'll be on my way" appearing on "Beatles Live at the BBC" Vol.1.
Listen also to the version on CD "That means a lot" reorded by "The Saltbee". They are the fantastic Swiss "Songs the Beatles gave away"-tribute band. "Saltbee" is an anagram which means a lot ...