Although very little is recorded about her early life, Eliza was was one of three known daughters of Edward Clement, a London shipwright. In about 1772, she married Anthony Fay, a barrister, and went to India with him. After separating from her husband in 1781/1782, Eliza Fay travelled extensively through France, Egypt, India, Italy, and New York. She made several voyages to Calcutta, and left letters and memoirs of her experiences that were published in the 20th century. They reveal great narrative power and include what E. M. Forster, as her editor, described as "little character sketches... delightfully malicious." Eliza Fay found her way into Calcutta society during her first period there, meeting several prominent people, including Warren Hastings.