His sons, Lovell Benjamin Badcock and William Stanhope Badcock went on to have distinguished military and naval careers, becoming a lieutenant-general and vice-admiral respectively, whilst his eldest daughter, Anne Badcock was married in 1809 to Major-General Sir Jasper Nicolls KCB.
He was married, in 1822, to Selina, daughter of Sir Henry Harpur Crewe of Calke Abbey, Derbyshire.
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His uncle, the merchant, Richard Badcock (d 1722), married Jane, the daughter of Sir Salathiel Lovell, from which line of the family came a number of prominent military and naval persons, including General Sir Lovell Benjamin Badcock and Vice Admiral William Stanhope Badcock.