Elizabeth was the youngest daughter of Augustus Berkeley, 4th Earl of Berkeley, by his Countess, Elizabeth daughter of Henry Drax, of Charborough (Dorset). On 30th May 1767, at her home in St. Martin-in-the-Fields, she married the Hon. William Craven, afterwards the 6th Lord Craven of Hamstead Marshall. Of this union six children were born, including William, the 2nd Earl of Craven. Lord and Lady Craven separated in 1780 and her ladyship left England for France, and travelled in Italy, Austria, Poland, Russia, Turkey and Greece. In 1789 she published in quarto her 'Journey through the Crimea to Constantinople' related in a series of letters.

Subsequently Elizabeth visited Anspach in Germany and took up her abode with Christian Frederick Charles Alexander, Margrave of Brandenburg, Anspach and Bareith, Duke of Prussia and Count of Sayn. She wrote to her husband that she was to be treated as the Margrave's sister. She wrote little plays in French for the Court theatre - 'La Folle du Jour' and 'Abdoul et Nourjad' - and, to further entertain the Margrave, translated, into French, the English comedy of 'She would and She would not.' Lord Craven dying in Lausanne (Switzerland) on 27th September 1791, his widow was married to the Margrave in Lisbon (Portugal), only sixteen days later. In 1792 the margrave sold his principality to the King of Prussia and settled in England, having purchased Brandenburg House in Hammersmith and the house and estate of Benham Park in Berkshire, which had long been possessed by the Craven family. The Margrave died of a "pulmonary complaint" at the latter on 5th January 1806 and was buried at nearby Speen Church.

Walpole, who always expressed his admiration of Lady Craven, and even addressed impromptu stanzas to her, furnished the Rev. William Mason with a lively account of the production of her comedy, the 'Miniature Picture' at Drury Lane in May 1780: "She went to it herself the second night in form, sat in the middle of the front row of the stage-box, much dressed with a profusion of white bugles and plumes, to receive the public homage due to her sex and loveliness. . . . It was amazing to see so young a woman entirely possess herself; but there is such an integrity and frankness in her consciousness of her own beauty and talents, that she speaks of them with a naiveté as if she had no property in them, but only wore them as gifts of the gods. Lord Craven, on the contrary, was quite agitated by his fondness for her and with impatience at the bad performance." Nevertheless it was the year of their separation. In 1785, Walpole wrote of Lady Craven to Sir Horace Mann: "She has, I fear, been infinitamente indiscreet, but what, is that to you or me? She is very pretty, has parts and is good-natured to the greatest degree; has not a grain of malice or mischief, almost always the associates, in women, of tender hearts, and never has been an enemy but to herself."

Lady Craven's first comedy, the 'Somnambule,' an adaptation from the French, was printed at Walpole's private press, at Strawberry Hill in 1778, and acted for a charitable purpose at Newmarket. In 1779, she published 'Modern Anecdotes of the Family of Kinvervankotsprakengatchdern, a Tale for Christmas,' a caricature of German pomposity, dramatized by WP Andrews. Others of Lady Craven's plays are the 'Silver Tankard,' a musical farce, produced at the Haymarket in 1781; and the 'Princess of Georgia,' presented on the occasion of Fawcett's benefit at Covent Garden in 1799. At the private theatre attached to Brandenburg House, the Margravine produced, in 1794, a comedy called the 'Yorkshire Ghost;' in 1799, a pantomime called 'Puss in Boots;' in 1805, a comedy called 'Love in a Convent' and other works. For these plays, the Margravine composed the music. As she wrote in her Memoirs, published in 1826: "My taste for music and poetry and my style of imagination in writing, chastened by experience, were great sources of delight to me. . . . Our expenses were enormous." The margravine often took part in the performances at Brandenburg House. In. 1796, the comedy of the 'Provoked Wife' was presented there, Mrs. Abington lending her services as Lady Fanciful, while the Margravine appeared as Lady Brute. The comedy was reduced to three acts and great importance was assigned to the character assumed by the Margravine. Mrs. Abington, however, insisted that certain of the excisions should be restored, so that her part of Lady Fanciful should not suffer. The Margravine died in Naples on 13th January 1828.