Originally Hannah Parkhouse, she was the daughter of Philip Parkhouse, a bookseller at Tiverton, Devon. At the age of about twenty-five, she married a Mr Cowley, an official of the East India Company; he died in 1797. Some years after her marriage, while at the theatre with her husband, she is said to have expressed the opinion that she could write as good a play as the one being performed, and within a fortnight she had written her first, The Runaway. She sent it to David Garrick, who produced it at Drury Lane in 1776.
Between then and 1795 she wrote twelve more plays, eleven of which were produced at Drury Lane or Covent Garden; and The Belle's Stratagem (1782), with one or two others, still survives in the list of acting plays. Among other pieces were Albina, Countess Raimond, A Bold Stroke for a Husband, More Ways than One, and A School for Greybeards, or The Mourning Bride.
Mrs Cowley also wrote poetry, mainly on historical subjects, and under the name of Anna Matilda, which has since become proverbial, she carried on a sentimental correspondence in the World with Robert Merry.