He was the eldest son of George Bingham, 3rd Earl of Lucan and Lady Anne Brudenell.
His maternal grandparents were Robert Brudenell, 6th Earl of Cardigan and Penelope Anne Cooke.
He became Lieutenant-Colonel of the Coldstream Guards and served as aide-de-camp to his father, who commanded the cavalry division during the Crimea War.
She was the youngest daughter of Charles Gordon-Lennox, 5th Duke of Richmond and Lady Caroline Paget.
They had seven children: He was succeeded in the title by his eldest son George Charles Bingham, 5th Earl of Lucan .