Cubitt joined the Institution of Civil Engineers as a member in 1823, became a member of council in 1831, vice-president in 1836, and held the post of president in 1850 and 1851. While president in 1851 he had major responsibility for the erection of the Great Exhibition building in Hyde Park. At the expiration of his services he was knighted by the queen at Windsor Castle on 23 December 1851. He became a Fellow of the Royal Society on 1 April 1830, and was also a fellow of the Royal Irish Academy, and a member of other learned societies.