It is the way our sympathy flows and recoils that really determines our lives. This opening sentence from Stuart Hall's 1960 review of Lady Chatterley's Lover belongs to DH Lawrence. The critic had unearthed it from deep inside the novel. It could serve as an epitaph for Stuart himself. His own sympathies and aversions played a huge part in determining his political makeup. It is not easy to sum up what he leaves behind in a few words. Soon, one hopes, that the conversation his colleague and friend, Bill Schwartz had been conducting with him over several years will be edited and published in book form.

He was, first and foremost, a political person. Politics mattered to him and enabled him to develop his skills as a mesmerising orator.

He was a 1956-er. The twin crises that erupted that year – the Anglo-French-Israeli invasion of Egypt and the Soviet intervention in Hungary – created a dissidence that spanned Europe. In Britain this led to the emergence of the first wave New Left, which resulted in magazines, the creation of New Left Clubs all over the country, and the Campaign for Nuclear Disarmament. Alongside Stuart, EP Thompson, Ralph Miliband, Raymond Williams, Doris Lessing and many others played their parts. When Stuart became the first editor of the New Left Review, with a strongly interventionist and activist approach, his message was clear. If you want change, get off your backsides and challenge the existing order, but also think, argue, debate as to best way forward. This remains an important legacy.

Hall first joined Birmingham University's centre for contemporary cultural studies under Richard Hoggart, whose brainchild it was; after the latter's departure from the centre Hall radicalised the project, half-joking to friends that his cultural studies project was politics by other means. The centre had started life by extending the tools of literary criticism to mass culture. Hall's more ambitious attempt was to develop a theory to analyse popular culture. This had a global impact, initially in the Anglo world, but later elsewhere. It also made him an inspirational figure for young black artists and film-makers in Britain, of whom Isaac Julien and John Akomfrah are the most prominent examples.

The politics of culture were put on the back burner for a while and replaced by a focus on the new politics that was abbreviated as Thatcherism. A set of powerful analyses followed in the pages of the Communist party journal, Marxism Today. Together with Eric Hobsbawm and Martin Jacques, he was a central figure in those debates that warned the left in the Labour party and outside that Thatcherism was a new phenomenon, an "authoritarian populism" that could not be defeated by traditional Labourist methods. It had to be understood before it could be contested. Many of the journals contributors (not Hall or Jacques) read the message in their own way and decided that contestation was no longer possible. They defected en masse, first to Neil Kinnock and then to New Labour, whose leaders attempted to render Thatcherism more profound and, in the process, killed off traditional social democracy. They were subjected to the withering scorn of Ralph Miliband in Socialist Register and the New Left Review.

Stuart remained a critic of the Blair regime and its successors, becoming more irascible as the years went by, warmly applauding the anti-Iraq war demonstrators and the students who occupied the universities soon after David Cameron's victory. Hall noted that no young Labour students had been involved in these actions, a clear sign that rigor mortis had set in.

In the oppressive aridity of neoliberal politics and culture, where the lies of its apologists are first worn as defensive masks but finally grow into their faces, his voice and his essays will be greatly missed. Unlike almost everyone else of his 1956 and later cohort, he did not write a book. Why, many asked, did he concentrate on the essay? Perhaps he liked the provisionality that lent itself to the shorter form. Or perhaps the masochistic practice of collective composition surrounded by sectarian twentysomethings at the Birmingham centre left him exhausted. I don't have the answer, but it doesn't really matter. There is much to explore in what he has left behind, especially the refusal to banish the political from everyday thought.

• This article was amended on 10 February 2014. The third paragraph incorrectly stated that Richard Hoggart was dead, this has been changed to reflect the fact that he had departed from Birmingham University's centre for contemporary cultural studies