He was the Sub-Chanter of York Cathedral for 47 years, as well as several other titles. He had 2 wives: (1) Susannah Walker (b.1726, Kirkheaton, Yorkshire, d.1761, York). (2) Sarah Heald (b.1732c. Otley, Yorkshire, d.1777 York). He had 2 children by 1st wife: Susannah Rockett (b. 1756 Bingley, Yorkshire, d.1759 York) & Rev. Dudley Rockett Jnr. (b. 1757, York, d. 1797 York).
He is probably from the Rockett clan of the Yorkshire area, but there is a possibility that he is from the Somerset clan of Rockett's, as he left his nephew Thomas Rockett of Taunton, Somerset, UK a large part of his Estate in his Will, as both his own children & wive's were deceased.