Her parents, Thomas Goddard, an heir to a Salisbury cutlery firm, and Arabella née Ingles, were part of an English community of expatriates living in Saint-Servan near Saint-Malo, Brittany.
[2] Her family suffered financial distress during the 1848 Revolution and had to return to England; there, Arabella had further lessons with Lucy Anderson and Sigismond Thalberg.
She made her formal debut on 14 April 1853, playing Beethoven's "Hammerklavier" Sonata, the first time the work had been performed in England.
From 1873 to 1876 she conducted a major tour, organised by Robert Sparrow Smythe,[5] of the United States, Canada, Australia, New Zealand, India, Shanghai, Hong Kong, Singapore and Java.
[6] In June 1874, while returning to Townsville, Queensland, from Java, her ship was wrecked, and she had to spend a night in an open boat in torrential rain with Charles Blondin, who was also arriving for an Australian tour.
[9] A number of composers dedicated pieces to her, including William Sterndale Bennett's Piano Sonata in A-flat, Op.