Alexander was the second son of Sir Francis Baring, a famous banker, and of Harriet, daughter of William Herring. He was brought up in his father's business, and became a partner at Hope & Co.. He was sent to the United States for various land deals, where he married (on 23 August 1798) Anne Louisa, daughter of William Bingham of Philadelphia, and formed wide connections with American houses. In 1810, by his father's will, he became head of the family firm. A year later when Henry Hope died, he merged the London offices of Hope & Co. into Baring Brothers & Co..
He sat in parliament for Taunton (1806–1826), Callington (1826–1831), Thetford (1831–1832), and North Essex (1832–1835). He regarded politics from the point of view of the business man, opposed the orders in council, "the restrictions on trade with the United States in 1812," in 1826 the act for the suppression of small bank-notes. He opposed reform. He accepted the post Chancellor of the Exchequer in the Duke of Wellington's projected ministry of 1832; but afterwards, alarmed at the men in parliament, declared "he would face a thousand devils rather than such a House of Commons."
He was Master of the Mint in Robert Peel's government, and on the latter's retirement was created Baron Ashburton on 10 April 1835, a title previously held by John Dunning. In 1842 he was again sent to America, and the same year concluded the Webster-Ashburton Treaty. A compromise was settled concerning the north-east boundary of Maine, the extradition of certain criminals was arranged, each state agreed to maintain a squadron of at least eighty guns on the coast of Africa for the suppression of the slave trade, and the two governments agreed to unite in an effort to persuade other powers to close all slave markets within their territories. Despite his earlier attitude, Lord Ashburton disapproved of Peel's free-trade projects, and opposed the Bank Charter Act of 1844.
He was a trustee of the British Museum and of the National Gallery, a privy councillor and D.C.L. He published, besides several speeches, An Enquiry into the Causes and Consequences of ... Orders in Council (1808), and The Financial and Commercial Crisis Considered (1847).
Baring and his wife had nine children: