Well, not really outtakes as such. More like "unreleased" artist demos. These two selections come from the first time The Beatles entered the EMI Studios in London (now called "Abbey Road" Studios). The date of the artist test was June 06 1962. The band consists of John, Paul, George and Pete Best. The first part of the artist test was conducted with Ron Richards behind the board and George Martin was called in after the second song (according to various sources).
The Beatles performed four tunes on this historic occasion. The first two songs exists but I don't know what happened to the tapes for the last two. The first song recorded was "Besame Mucho". For some reason, I just don't understand why The Beatles would perform the same song that they performed for the Decca Audition earlier in January of that year. The song is latin flavoured and really does not represent the band's direction at the time. Maybe they just liked the song. Paul on vocals for this one.
The next tune recorded was a version of "Love Me Do". An original where John sang the title line at first but it intruded with his harmonica playing so Ron Richards made Paul sing the line. The two last songs recorded were "P.S. I Love You" and "Ask Me Why". All originals with the exception of the first song. Both latter titles would end up on the B sides of the first two singles.
The version of "Besame Mucho" would end up as a possibility for the early 1980s EMI "Sessions" project and be released on the bootleg of the same name. The version of "Love Me Do" comes from an acetate found at George Martin's home in 1994 (WTF ???) and was used on the 3-LP/2-CD "Anthology 1" issue.
This is also the first and last time Pete Best recorded at EMI with The Beatles. George Martin was not impressed with his drumming skills. Simply listen to "Love Me Do" on "Anthology 1" and you will see why.