His father, another George, married (1793) Selina, daughter of Henry Peckwell (1747–1787), minister of Selina, Countess of Huntingdon's chapel in Westminster, and his wife Bella Blosset (descended from a Huguenot officer Salomon Blosset de Loche who left the Dauphiné on the revocation of the Edict of Nantes), and had one daughter and ten sons, of whom George was the eldest.
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His grandfather, Andreas, originally a Bremen merchant, was one of the founders (on 1 January 1766) of the banking-house of Grote, Prescott & Company in Threadneedle Street, London (the name of Grote did not disappear from the firm till 1879).
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He settled in 1820 in a house attached to the bank in Threadneedle Street, where his only child died a week after its birth.
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By her he had a son, Robert Henry, and a daughter, Selina Mary (named after her godmother, the Countess of Huntingdon), who, in 1793, married George Grote, the banker, and became the mother of George Grote and Arthur Grote.
In opposition to Otto Gruppe, he denied that Plato affirmed the diurnal rotation of the earth (Untersuchungen über das kosmische System des Platon, 1852), and when in opposition to him Grote published his opinions on the subject (Plato and the Rotation of the Earth) Böckh was ready with his reply.
Individuals within this group included Francis Place (1771–1854), George Grote (1794–1871), Joseph Parkes (1796–1865), John Arthur Roebuck (1802–1879), Charles Buller (1806–1848), John Stuart Mill (1806–1873), Edward John Trelawny (1792–1881), and William Molesworth (1810–1855).