John Grigg was the son of Edward Grigg, a Times journalist associated with the imperialist circle of Joseph Chamberlain, Conservative MP, governor of Kenya, and member of Churchill's wartime government, who was created first Baron Altrincham in 1945, and his wife Joan Dickson-Poynder, the daughter of Lord Islington. From Eton, John Grigg joined the army and was commissioned into the Grenadier Guards. While in the army, Grigg served as officer of the Guard at St. James Palace and Windsor Castle and saw action against the Germans in France and Belgium.

After the war Grigg attended New College, Oxford, where he read Modern History. While there, he gained a reputation for academic excellence, winning the University Gladstone Memorial Prize in 1948. Upon graduation, Grigg joined National Review, which was owned and edited by his father. As Altrincham's health failed, his son assumed most of the managerial and editorial duties before formally taking over the editorship of the now-renamed National and English Review in 1954.

A liberal Tory, Grigg entertained hopes of election to the House of Commons. He stood for election for the recently created Oldham West in the 1951 general election, but was defeated by the sitting member Leslie Hale. Grigg contested the seat again in the 1955 general election but was similarly unsuccessful. With his father's death in 1955, Grigg inherited the title of Baron Altrincham, which seemingly ended any hope of election to the House of Commons. Nonetheless, Grigg refused to apply for a writ of summons, abjuring his right to his seat in the House of Lords.

His father's death freed Grigg to edit the National and English Review into a publication more reflective of his views. In 1956 he attacked the Conservative government for its handling of the Suez crisis and pressed for an immediate withdrawal of British forces from the area. He followed his father in championing reform of the House of Lords, though he added that, in lieu of reform, abolition might be the only alternative. But Grigg stirred what was perhaps his greatest controversy when, in August 1957, he argued in an article that the Queen's court was too upper-class and British, and instead advocated a more "classless" and Commonwealth court. More personally, he attacked the Queen's style of speaking as "a pain in the neck": "Like her mother, she appears to be unable to string even a few sentences together without a written text...The personality conveyed by the utterances which are put into her mouth is that of a priggish schoolgirl, captain of the hockey team, a prefect, and a recent candidate for Confirmation".

Grigg's article caused a furor and was attacked by the majority of the press, with a minority, including the New Statesman and Ian Gilmour's The Spectator, agreeing with some of Grigg's ideas. Henry Fairlie of the Daily Mail, attacked Grigg for "daring to pit his infinitely tiny and temporary mind against the accumulated experience of centuries". The Archbishop of Canterbury, Geoffrey Fisher, also attacked Grigg. When Grigg was leaving Television House, after giving an interview defending his article, a member of the League of Empire Loyalists came up to him and slapped his face, saying: "Take that from the League of Empire Loyalists". The man, Philip Kinghorn Burbidge, was fined 20 shillings and said: "Due to the scurrilous attack by Lord Altrincham I felt it was up to a decent Briton to show resentment".

In 1960 the National and English Review ceased publication as a result of financial difficulties. Grigg moved to The Guardian, where he worked as a columnist for ten years. When Viscount Stansgate succeeded in obtaining passage of the 1963 Peerage Act, Grigg was the second person (after Viscount Stansgate himself) to take advantage of the new law and disclaim his peerage. Yet he never achieved his ambition of election to the Commons, and he subsequently left the Conservative party for the SDP in 1982. He also worked as a columnist for The Times from 1986 until 1993 and wrote occasionally for The Spectator.

By the late 1960s, Grigg turned his attention to the project that would occupy him for the remainder of his life: a multi-volume biography of the British prime minister David Lloyd George. The first volume, The Young Lloyd George, was published in 1973. The second volume, Lloyd George: The People's Champion, which covered Lloyd George's life from 1902 to 1911, was released in 1978 and won the Whitbread Award for biography for that year. In 1983 the third volume, Lloyd George, From Peace To War 1912-1916, was published and subsequently received the Wolfson prize). When he died in 2001 Grigg had nearly completed the fourth volume, Lloyd George: War Leader, 1916-1918; the final chapter was subsequently finished by Margaret MacMillan and the book published in 2002. In all the volumes, Grigg showed a remarkable sympathy, and even affinity, for the "Welsh Wizard", despite the fact that their domestic personalities were very different.

Grigg also wrote a number of other books, including a biography of Nancy Astor, Volume VI in the official history of The Times covering the Thomson proprietorship, and The Victory that Never Was, in which he argued that the Western Allies prolonged the Second World War for a year by invading Europe in 1944 rather than 1943.