While attending school in Bodmin, William's talent for drawing attracted the attention of the Prior Colonel Walter Raleigh Gilbert’s wife.
Clift arrived in London on 14 February 1792 and was taken on as an unpaid apprentice "to write and make drawings, to dissect and take part in the charge of the museum" which his master had established at the back of his house in Leicester Square.
His only daughter, Caroline Amelia Clift, was married at New St. Pancras Church on 20 July 1835 to Professor (later Sir Richard) Owen, and died at Sheen Lodge, Richmond Park, on 7 May 1873, age 70.
'[citation needed] Benjamin Brodie the elder praised his industry and his thirst for the acquisition of knowledge, his sagacity and keen observation.
Clift's drawings were featured in A Series of Engravings … to illustrate the Morbid Anatomy of some of the most important parts of the Human Body, by Matthew Baillie.
Its initial advertisement announced that 'the drawings will be made by a young man, who is not only very well skilled in his own arts, but who possesses a considerable share of knowledge in anatomy.'
Dr. Westby-Gibson is the owner of two manuscripts in shorthand, giving the particulars of forty-nine lectures delivered by Dr. Haighton at Guy's Hospital 1814–15, which are believed to be the work of Clift.
His portrait, from a daguerreotype, is in Claudet's Historical Gallery and his bust in plaster, with the date 1843, is placed on the entrance door to the western museum of the College of Surgeons.