The next two years or so would be the busiest years for the Beatles with a various amount of radio appearances, television and concerts and finally recording. On January 22 1963, the Beatles played live at the BBC for their debut on the program "Saturday Club".
The Beatles ended up playing both of their A-sides singles up to that point: "Love Me Do" and "Please Please Me". They also performed three covers including "Some Other Guy", "Keep Your Hands Off My Baby" and "Beautiful Dreamer". The host for this particular show was Brian Matthew and the location of the performance was a the Playhouse Theatre in London.
The three cover songs can be found on the bootleg LP "Beautiful Dreamer". The first A-side single "Love Me Do" can be found on the CD bootleg box set "Mythology, Volume 1". The second A-side single has not yet been released as this performance.