Born Algernon Smithson, he was the second son of the 1st Duke of Northumberland (of the third creation) and his wife, Elizabeth and was educated at Eton. In 1774, he was elected MP for Northumberland and a year later, he married Isabella Burrell, a sister of the future 1st Baron Gwydyr. Their surviving children were:
In 1786, he left the Commons when he inherited his father's barony of Lovaine (a title which was created for his father with a special remainder to pass to Algernon as a second son) and was promoted in the Peerage as Earl of Beverley in 1790. On his death in 1830, his titles passed to his eldest son, George, who later inherited the dukedom of Northumberland from his cousin, the 4th Duke, in 1865.