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Appointed in 1948 to the department of drama at Bristol University (the UK's first such department), he convened a 1951 symposium on "the responsibility of universities to the theatre" to endorse the policy of studying drama in the context of theatre and a 1954 symposium on "the relationship between universities and radio, film, and television". He also did the groundwork for the university's theatre collection in 1951 (which now has museum status and a major archive). In 1955, he was made the department's head and in 1960 took up its chair of drama. He also helped to set up a playwriting fellowship in the department, attracting young playwrights like John Arden, and premiered Harold Pinter's first play, The Room in 1957. At his death he was the department's professor emeritus.
Glynne served as president of the American Society for Theatre Research from 1976 to 1999. In 1970 his advice was sought by Sam Wanamaker on the setting up of Shakespeare's Globe. In 1999 he was awarded the Sam Wanamaker Prize. The Standing Conference of University Drama Departments's postgraduate scholarship and Bristol University's studio theatre are both named after him, as is an annual lecture under the joint auspices of the Society for Theatre Research and the Drama Department at Bristol to mark his service to them both.
- Shakespeare's Dramatic Heritage (1969)
- The Medieval Theatre (1974)
- English Moral Interludes (1975)
- A History of the Theatre (1985)
- English Professional Theatre, 1530-1660 (2001) (editor and co-author)