He was born Lovell Benjamin Badcock, the eldest son of Thomas Stanhope Badcock of Little Missenden Abbey, Buckinghamshire and Maplethorpe Hall, Lincolnshire.
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Interestingly, there is no known familial relationship between Lovell Benjamin Badcock and another prominent nineteenth century British Army general bearing the same surname - General Sir Alexander Robert Badcock.
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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.
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.