In the 1930s, the LSE was the academic home of the most famous economic argument of the twentieth century. On one side was John Maynard Keynes at Cambridge, who would soon publish The General Theory and argue that governments must actively manage demand to escape depressions. On the other was Friedrich Hayek, an Austrian who had joined the LSE faculty in 1931, arguing — alongside his colleague Lionel Robbins — that free trade and minimal state intervention were the only sustainable answer, and that Keynesian stimulus would seed future instability. The debate started over the immediate question of how to address the Great Depression. It expanded into a fundamental disagreement about what economics itself was for. Both Hayek (in 1974) and James Meade (in 1977), an LSE lecturer from 1947, would eventually win Nobel Memorial Prizes in Economic Sciences. So would John Hicks (in 1972) and Arthur Lewis (in 1979), the LSE's first Black academic, who became the only Black person ever to win the Nobel Prize in Economics. As of 2025, the school is affiliated with 21 Nobel laureates.

In 1942, the director of the London School of Economics produced a report. It was called Social Insurance and Allied Services. The author was William Beveridge, an Oxford-trained social reformer who had run the LSE from 1919 to 1937. The Beveridge Report identified five 'giant evils' afflicting British society — want, disease, ignorance, squalor, and idleness — and proposed a comprehensive system of social insurance to combat them. It became the founding document of the British welfare state. Clement Attlee — who had himself lectured at the LSE before entering politics, and who had been shocked into socialism by his earlier years working with slum children in Limehouse — implemented Beveridge's recommendations as Prime Minister from 1945 to 1951. The National Health Service, free at the point of use, opened on 5 July 1948. It came, in significant part, from a desk at 14 Houghton Street. Since 1990, LSE has educated 24 prime ministers or presidents, the second-highest figure for any UK university — and since 1895, over 40 world leaders have studied or taught there.

In 1966 the school appointed Sir Walter Adams as its new director. Adams had previously been principal of the University College of Rhodesia and Nyasaland. The student union objected, citing his failure to oppose Rhodesia's Unilateral Declaration of Independence under Ian Smith's white minority government, and his cooperation with that regime. Protests broadened to wider concerns about LSE's investments in Rhodesia and South Africa, and about the school's response to its own students. On a January day in 1969, students tried to dismantle the school gates. Over thirty were arrested. The LSE closed for 25 days. Injunctions were taken out against thirteen students; three were ultimately suspended; two foreign students were deported; two staff members seen as supportive of the protests were dismissed. The LSE that emerged was bruised, but the institution survived. By the time the 1970s ended, those four Nobel laureates I mentioned above had all received their prizes.

Not all of the LSE's twenty-first century has gone smoothly. In February 2011, director Howard Davies resigned over the school's relationship with Saif al-Islam Gaddafi, son of the Libyan dictator Muammar Gaddafi. The LSE had matriculated Saif and accepted a £1.5 million donation from his family. As the Libyan revolution unfolded and Gaddafi's regime crumbled, the propriety of those decisions became impossible to defend. Lord Woolf, the former Lord Chief Justice, was asked to investigate; the report was damning. In 2017, contracted cleaners working through Noonan Services struck for weeks demanding employment rights equivalent to in-house staff; commentator Owen Jones refused to cross the picket line on his way into a public debate with Peter Hitchens. By June 2018 some 200 outsourced workers had been brought back in-house. In 2024 leaked emails surfaced in which senior LSE staff described students wearing keffiyehs at protests over the school's investments in Israel as 'dressed as terrorists.' Universities, like the societies they sit in, contain their own internal politics. The LSE's reputation rests in part on being honest about that.

The school occupies an almost continuous group of around 30 buildings between Kingsway and Aldwych, in the historic area of Clare Market. King George V laid the foundation stone of the Old Building in 1920. The campus now includes the Saw Swee Hock Student Centre (opened January 2014, designed by O'Donnell & Tuomey, BREEAM 'Outstanding' rated and shortlisted for the Stirling Prize), the 13-storey Centre Building by Rogers Stirk Harbour and Partners (opened June 2019), and the Marshall Building by Grafton Architects (opened January 2022). The British Library of Political and Economic Science — the LSE Library — is one of the largest social science libraries in the world. The school operates under a Latin motto from Virgil's Georgics: rerum cognoscere causas, 'to know the causes of things.' The beaver, the school's official mascot, was adopted in 1922 on the recommendation of a twelve-person committee, eight of whom were students. The endowment grew from £113 million in 2015 to £255 million in 2024 — the sixth-largest of any UK university — with annual income reaching £548.2 million in 2024/25. The Fabians who started this with someone else's £20,000 would, I think, be quietly satisfied.