He was educated at the independent (and at the time "boys-only") school Christ's Hospital in the countryside near Horsham, West Sussex (which he found difficult because of his Jewish origins), and at the London School of Economics, where he contributed to the student newspaper The Beaver.
His talent was spotted in 1955 when he was offered a column in The Manchester Guardian. He wrote (as "Taper") a political column for The Spectator from 1956 until 1962, his departure being a shock to many who saw him as a natural successor for the magazine's editorship. He later wrote for The Daily Express and, from 1962 to 1970, for The Daily Mail; he resigned from the latter in June 1970, citing differences with the newspaper's management during the general election of that year.
His longest-standing appointment was his column for The Times from 1971 to 1997. This became a platform for his passionate liberal views and his scorn for authoritarianism of both left and right. In 1981 he took a self-imposed sabbatical from the newspaper after a disagreement over the selection of a new editor as successor to William Rees Mogg. He was coaxed back twelve months later after The Times came under different editorial control. On his return, he began his column with "And another thing." His frequent mention in his column of his favourite composer Richard Wagner became something of a standing joke (although he also often expressed his admiration for Mozart as well). His sympathy for East European dissidents during the Soviet era was also frequently expressed, as also his vociferous disapproval of the apartheid regime in South Africa. He was a regular habitué of the Royal Opera House, Covent Garden. Other recurrent themes were the poor standards of service offered by the public utilities (his merciless mockery of the North Thames Gas Board became a cause celèbre), his love of fine dining, and his support for homosexual rights despite being himself entirely heterosexual.
Levin appeared regularly on television, including the series Face The Music and That Was The Week That Was (TW3). In the latter, he interviewed prominent politicians and influential thinkers of the day, usually with the lack of reverence which was the programme's hallmark. He was awarded his CBE for services to journalism in 1990.
He was renowned for his acerbic wit. In 1963, during the live weekly edition of TW3, he was physically assaulted by the Hon Desmond Arthur Peter Leslie, a member of the audience, for allegedly insulting his then wife, the actress Agnes Bernelle, in an article he had written. The video of this event is available here: . His activities also got him blackballed when he tried for membership of the Garrick Club. In 1971 he wrote an article in The Times called "Judgement on Lord Goddard" attacking the recently deceased former Lord Chief Justice.
Levin never married, but had many girlfriends. He dated (and later lived with) fellow Face The Music panelist Arianna Stassinopoulos (now known as Arianna Huffington) from 1971 until she left him in 1980 (saying later this was partly because he refused to marry her). Writing in The Sunday Times after his death, she described Levin as "the big love of my life". She was junior to him by more than 20 years.
Levin began to have difficulty with his balance as early as 1988, although Alzheimer's Disease was not diagnosed until the early 1990s. He was nursed through the long degenerative phase of the illness by his long-term partner Liz Anderson, until his death. Anderson was also junior to him by more than 20 years.
Society of Indexers in England has instituted an award in his name. His book reviews often contained comments on the quality of a book's index.
Levin's polemical writings enjoyed fame which few journalists have matched. One commentator called him the best English journalist since G. K. Chesterton.