Taylor White was born at his family's seat in Wallingwells, a hamlet in North West Nottinghamshire. He was one of the five children, and the second son, of Thomas and Bridget (née Taylor) White. His father was for many years the Member of Parliament for East Retford and in 1717 was appointed Clerk of the Ordnance. His maternal grandfather, Richard Taylor, was the High Sheriff of Nottinghamshire and had also served as the Member of Parliament for East Retford. White was admitted to Lincoln's Inn in 1720 where he studied law and was called to the bar in 1727. He practised as a barrister on the Northern Circuit (Yorkshire, Northumberland, Cumberland and Westmoreland) and eventually received several judicial appointments including Circuit Judge on the North Wales Circuit (1750) and Puisne Justice of Chester (1760). In 1737 he had also been one of the four counsels retained by Georgia (then a British colony) in a dispute with its neighbouring colony South Carolina over trade with the Indians.

A friend and associate of the British philanthropist, Thomas Coram, White worked tirelessly to raise funds enabling the establishment of Coram's Foundling Hospital in 1739. He became one of the founding Governors, and it was in White's London house that the announcement for its first intake of infants was drawn up. Along with Coram and the Duke of Richmond, White and his fellow Governors were present on the evening of 25 March 1741 when the first children arrived. He became a key figure in running the institution, serving as its Treasurer from 1745 until his death, and was largely responsible for the establishment of the Hospital's branch in Ackworth, West Yorkshire. A portrait by Francis Cotes of White working on his ledgers hung in the Committee Room of the Hospital along with works by william Hogarth and George Lambert, and is now in the care of the Foundling Museum. A keen art collector himself, White was instrumental in building up the Hospital's famous art collection, persuading many of the leading artists and Collectors of the day to donate works to it. He also commissioned a large marine painting from Charles Brooking for the Committee Room and a painted glass window from william Peckitt for the Hospital's chapel.

Upon his death on 27 March 1772, White was succeeded by his eldest son, also named Taylor White, in his substantial estates. He was buried in the family church in Tuxford.