Complex sentence: The family was extremely well-off and he was educated at home by a governess until he was nine, when he began composing; his musical talents being "obvious" by the time he went up to Gonville and Caius College, Cambridge in 1924.
Split into simpler sentences: The family was extremely well-off and he was educated at home by a governess until he was nine, when he began composing. His musical talents became "obvious" when he went up to Gonville and Caius' College, Cambridge in 1924.