Complex sentence: By age 13, Willy Russell was leaving school during school times to go to the "Cavern" and attend sessions there; during his time at the Cavern he was introduced to the works of The Beatles.
Split into simpler sentences: By age 13, Willy Russell was leaving school (during school time) to go to the "Cavern" and attend sessions there. During his time at the "Cavern" he was introduced to the works of The Beatles.