Leeson, Joseph (1660–1741), brewer and property speculator, was the youngest of four sons of Hugh Leeson and his wife, Rebecca Leeson, daughter of Richard Tighe, MP and mayor of Dublin. His father, who was born in Culworth, Northamptonshire, and who had been in the army, was probably in Ireland by 1660, establishing himself as a brewer near St Stephen's Green in Dublin.
Leeson inherited his father's brewing interests, which expanded under his direction. The family name in his time came to be attached to the south side of St Stephen's Green (Leeson's Walk), the lands behind (Leeson's Fields), and finally to Leeson Street. His property interests, however, appear to have extended much more widely. Jonathan Swift (qv) accused him of taking advantage of builders in financial difficulty by buying unfinished houses in Dublin at bargain prices for ready cash. He also acquired lands in several counties, and his wealth was the foundation of the rapid social ascent of the next generation of his family. In 1695 he married Margaret Brice, daughter of Andrew Brice, an alderman and sheriff of Dublin. They had six surviving children: five daughters and one son, also Joseph Leeson (qv), the heir.