In the summer of 1971, one of the first Beatles bootlegs turned up, packaged in a white sleeve with “The Beatles — Yellow Matter Custard — Previously Unreleased Studio Material” rubber-stamped across it. It offered an odd lineup of tracks (performances of Ray Charles’s “I Got a Woman”; Buddy Holly’s “Crying, Waiting, Hoping”; Carl Perkins’s “Sure to Fall (in Love With You)”; Arthur Alexander’s “Shot of Rhythm and Blues”), 14 in all, in decent, if slightly tinny, quality.

Beatles scholarship was in its infancy then, and collectors had no idea what these tracks were. When a fan played the disc for John Lennon in 1972, he said it was the Beatles’ failed Decca audition from a decade earlier. He was wrong. By the late 1970s, the recordings’ provenance was established: The Beatles recorded these songs in 1963 for a 15-week BBC radio series, “Pop Go the Beatles.”

Few American fans knew of the half-hour show, or knew that the Beatles performed regularly for the BBC from 1962 to 1965, and British fans rarely mentioned it. On both sides of the Atlantic, the Beatles narrative focused instead on the group’s amazing musical development, as captured in its EMI studio recordings.

But the BBC was crucial to the Beatles’ career. It presented them on its airwaves months before they had a record deal, and when it offered them “Pop Go the Beatles,” the group had released only three singles and one LP.