Sir George Downing, 2nd Baronet, of East Hatley was the son and heir of Sir George Downing, 1st Baronet.
His father worked as Teller of the Receipt of the Exchequer from 1660 until 1684. In 1680, the younger George Downing joined his father as a Teller of the Receipt of the Exchequer, holding that position until April 1689. His father died in July 1684, and the younger Downing inherited his father's baronetcy.
Sir George Downing, 2nd Bt. married Lady Catherine Cecil, daughter of James Cecil, 3rd Earl of Salisbury. The couple had one son, Sir George Downing, 3rd Baronet.