Early in her literary career she wrote a number of light farces, pantomimes, and fables, many of which were performed in London to no great acclaim. She knew Samuel Johnson and James Boswell, and became a close friend of Horace Walpole, who published her early works which, with later efforts, include:

• The Sleep-Walker (trans. of Pont de Vile's comedy La somnambule, 1778)
• Modern Anecdotes of the Ancient Family of the Kinkvervankotsdarsprakengotchderns (satire, 1779)
• The Miniature Picture (play, 1781)
• A Journey through the Crimea to Constantinople (travel writing, 1789)
• The Georgian Princess (produced 1798; published 1799). Ed. with an introduction by John Franceschina. British Women Playwrights around 1800. 15 January 2001.
• Letters from the Right Honorable Lady Craven, to his serene highness the margrave of Anspach, during her travels through France, Germany, and Russia in 1785 and 1786 (travel writing, 1814)
• Memoirs (1826)

Very little of her musical compositions survive:

• O Mistress Mine (musical arrangement, about 1875)
• The Princess of Georgia (opera, 1799)

Her life was full of scandal: after thirteen years of marriage, six children, and affairs reported on both sides, she and her first husband, William Craven, 6th Baron Craven, (married since 30 May 1767), parted permanently in 1780. Thereafter she lived in France and travelled extensively on the Continent.

For a number of years she was in a relationship with Alexander, Margrave of Brandenburg-Ansbach and Bayreuth. His wife since 1754, Princess Friederike of Saxe-Coburg-Saalfeld, died in Germany on 18 February 1791, and Lady Craven's husband died in Lausanne on 26 September 1791. The couple married in Lisbon on 30 October 1791. They settled in England and while the Margravine was snubbed by ladies mindful of their reputations, as well as by her latest husband's cousin, George III himself, the couple lived a busy and opulent life in Hammersmith, London and Benham Park at Speen in Berkshire.

Nonetheless, Elizabeth was never legally entitled to share her husband's German rank and title: On 20 February 1801, she was granted the morganatic title of "Princess (Fürstin) Berkeley" by the last Holy Roman Emperor Francis II. In fact, Christian Frederick, being the last of his cadet branch of the House of Hohenzollern, and childless, had exchanged his hereditary birthright to the appanages of Ansbach and Bayreuth for an annuity of 300,000 guilders from his pater familias, King Frederick William II of Prussia, a month after his second marriage. In England, however, the couple were usually known as the "Margrave and Margravine of Brandenburg-Ansbach".

After the Margrave's death at Benham Park in 1806, his widow moved back to the Continent, to Naples, where she died at Craven Villa in Posillipo, and was buried in 1828 in the English Cemetery. Her links with the Hammersmith area are commemorated in the name of two roads in the area - Margravine Gardens and Margravine Road.