Complex sentence: When the Woolfson-sung songs became significant hits, the record company pressured Parsons to use him more, but Parsons preferred "real" singers, which Woolfson admitted he was not.
Split into simpler sentences: When the Woolfson-sung songs became significant hits, the record company pressured Parsons to use him more. However, Parsons preferred to use more technically polished and proficient singers, which Woolfson admitted he was not.