Head of UK policy for the charity, Sally Copley, said: "Children who do after-school activities have more confidence, see the world in different ways, have a stronger sense of identity - and this ultimately translates into doing better in exams and getting a better job.
"We're particularly concerned poorer children are missing out as a result."
Children of parents with professional jobs were nearly twice as likely to have music lessons than children in a household with a gross income lower than £15,000 a year, the charity says.