Wainewright was born in 1794 at Richmond, Surrey into affluence and London literary society in Richmond, London, England but was orphaned when he was very young.
His father's identity has never been firmly established. He may have been an apothecary, although it is more likely that he was a lawyer and came from a family that practised the law over many years. His mother died giving birth to him, but of her interesting background we have a very complete picture. She was Ann, the daughter of Ralph Griffiths (1720-1803), for many years the editor of The Monthly Review.
Thomas and his father lived in an extended family situation with his maternal grandfather at Linden House at Turnham Green in what was then London's rural periphery. Griffiths was well connected in the literary world and Thomas must have profited from the society that visited Griffiths' home. When Griffiths wrote his will in 1803 Thomas's father was already dead and he himself died later in that year.
The child then came under the care of his maternal uncle, George Griffiths.