Drew was born in London. He received his early training in dance at the Westbury School of Dancing in Bristol, before entering professional ballet training at the Royal Ballet School. He has been a dancer with The Royal Ballet for the entire duration of his career, joining the company in 1955, and being promoted twice, to Soloist in 1961 and then to Principal in 1974. He retired from The Royal Ballet as a Principal dancer following the 2002/2003 season, but remained with the company as a Principal Character Artist and in recognition of his long service to the company, he also has the honorary title of Guest Artist. Drew is a teacher of pas de deux at the Royal Ballet School, the founder President of the Ballet Association, and in 2006, he was awarded the MBE for services to dance. He is married to actress June Ritchie.