Allen was born as Marie Anita Bazzi in Westminster, London, England in July of 1891. Her father was a Swedish restaurant proprietor named Giuseppe Bazzi and her mother was named Marie Bazzi. Allen married fellow English stage actor, Henry Marsh Allen, in 1913 and they had one son together. Mary was a frequent collaborator of film director Arrigo Bocchi and worked under Windsor Film Company. In 1919, Mary started her own production company named Mary Marsh Allen Productions. Under the company, she produced the film Forgive Us Our Trespasses (1919); she and her husband also starred in it.