He is the son of an actress turned schoolteacher, Jenny Davis, and Patrick Dromgoole, theatre director and television executive.
[4] His directing credits during this time included Troilus and Cressida, 50 Revolutions, Anton Chekhov's Three Sisters, Rookery Nook by Ben Travers and August Strindberg's Easter.
[9] In January 2014 he directed The Duchess of Malfi, the opening production at the Sam Wanamaker Playhouse (the Globe's indoor counterpart).
He was replaced by Emma Rice[13][14] Following his departure from the Globe, two of his productions, Farinelli and Nell Gwynn, transferred to the West End.
[17] In 2019 Classic Spring announced that Dromgoole would be adapting and directing a double bill production of Frankenstein and Dracula at the Hackney Empire in 2020.
[18] In 2023 he directed Jordan Harrison's play, once filmed, Marjorie Prime at London's the Menier Chocolate Factory described by the Guardian as 'elegant'.