Statesman and lawyer. The son of Patrick Hume of Polwarth, 1st Earl of Marchmont (1641 - 1724), he spend his youth in the Netherlands, where his father was living in exile. He studied law at Utrecht before returning to Scotland in the early 1690s. Hume was admitted to the Faculty of Advocates in 1696. The following year he married Margaret, daughter and heiress of Sir George Campbell of Cessnock in Ayrshire, and adopted the name Campbell.
Hume-Campbell was a member of the Scottish Parliament for Berwickshire and sat in the last session before the Treaty of Union of 1707, which he strongly supported. In 1712, he went to Hanover to smooth the way for the succession of the Elector as King George I of Britain. He was appointed Lord-Lieutenant of Berwickshire in 1715, and at the breaking out of the rebellion raised a Berwickshire militia of four hundred in defence of the Hanoverian succession.
He was knighted as Sir Alexander Campbell of Cessnock, was appointed to the Bench as Lord Cessnock and became Earl of Marchmont on the death of his father in 1724. He was created a Knight of the Order of the Thistle (1725).
He served as ambassador to Denmark (1715-21), Lord Clerk Register of Scotland (1716-33), as one of the British ambassadors to the Congress of Cambrai (1722-24), a meeting of the major European powers to resolve the conflict between Holy Roman Emperor Charles VI and King Philip V of Spain.
Hume-Campbell was elected one of the Scottish representative peers in 1727 but, with other Scottish nobles, incurred the wrath of Prime Minister Robert Walpole by blocking his excise scheme. He was dismissed from his offices and not re-elected in 1734. Questions were asked about government for interference in the election of the Scotch peers.
He died in London but was buried in the churchyard of Canongate Kirk in Edinburgh. He was succeeded by his third son, Hugh Hume-Campbell as the 3rd Earl of Marchmont, the last in the line.
