Interesting notes from Richie Unterberger. Quoted:
For about 25 years after the event, an almost poetically perfect story of how the Beatles' first chart-topping single arose was accepted as gospel. George Martin, the story went, wanted The Beatles to record How Do You Do It -written by Mitch Murray, a songwriter from the Britisch equivalent of Tin Pan Alley- as their second single. The Beatles hated the song. George Martin made them record it anyway. The Beatles, however, insisted they had something better, and played him something they'd written, Please Please Me; it went to No. 1 in Britain; not only was the Beatles' judgment vindicated, but their ability to write their own material would never again be questioned. The story crumbled, however, when it was discovered, with the aid of unimpeachable EMI paperwork, that in fact Martin had wanted to release How Do You Do It as their first single. It was Love Me Do that the Beatles persuaded him to release instead. [...]
It's been said that the Beatles deliberately fouled up their recording of How Do You Do It to roadblock its release. As Paul McCartney said in Barry Miles's biography Many Years From Now, 'We knew that peer pressure back in Liverpool would not allow us to do How Do You Do It. We know we couldn't hold our heads up with that sort of rock-a-pop-a-ballad. We would be spurned and cast into the wilderness." As new, unproven recording artists, however, they really weren't in the position to be so obstinate. They did learn the number at Martin's request in advance of their EMI session, even performing it (presumably for a very brief period) live. When they did record it, they didn't so much screw it up as sound uninspired, albeit deliberately so.