Final answer:
Allen Klein managed both The Beatles and The Rolling Stones at different points in their careers, making him the correct answer to the question.
Step-by-step explanation:
The individual who managed both The Beatles and The Rolling Stones at one point in time is Allen Klein.
Andrew Oldham is often associated with the Rolling Stones as their early manager and producer, while Brian Epstein is famously known for managing The Beatles until his death in 1967. Malcolm McLaren was associated with the punk scene and managed the Sex Pistols.
Thus, Allen Klein is the correct answer to the question.