From 1781 he was resident in Dublin, along with his family who also acted, and he wrote a history of the Irish stage.
Hitchcock and his wife Sarah were members of the company at the Theatre Royal, Norwich from 1769.
From 1777 they were at George Colman the Elder's Haymarket Theatre, where he was prompter, while his wife and daughter Mary Anne both acted; during the winter seasons they continued to appear at York.
Hitchcock was the model for the prompter in George Colman the Elder's play The Manager in Distress (1780).
His daughter Mary Anne retired from the stage on her marriage to a Dublin barrister, Jonas Greene.