Born Henry Silvertop, he married Eliza, daughter of Thomas Witham, esq. of Headlam, in the county of Durham, and niece and heiress of William Witham, esq. of Cliffe, in Richmondshire, North Yorkshire, and thus inherited the Witham name and Coat of arms. Though having no botanical training, he applied to plants James Nicol's method of examining rocks by slicing thin sections of them. His findings were published in his 1833 book The Internal Structure of Fossil Vegetables found in the Carboniferous and Oolitic deposits of Great Britain, illustrated by William MacGillivray.
He worked strenuously for the Mechanics Institute, which provided education for the working classes and the Relief of the Sick Poor.