British History Online gives: "Robert Dingley (d. 1742), a City goldsmith, acquired a small house in North End in 1727 and a grant of waste in 1738. He left the estate to his younger son Charles, who made a fortune out of trade with Russia and by 1769 had bought buildings and pieces of waste in Hampstead in 17 separate lots ... but Dingley, put up as a candidate to oppose Wilkes, died in 1769 after being beaten up by the mob...."
See Pitt House for information about his house in Hampstead's North End. Most of his estate there, including Pitt House, was bought in 1787 by Abraham Robarts.
The ODNB has a page for his brother Robert, which gives some information about Charles: He "projected London's New Road and New City Road (1756–61), received the Society of Arts gold medal in 1768 for building a large sawmill at Limehouse."
It was this last activity that brought on him the satirical cartoon, in which he is sawing away the structure on which he stands.
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