Hampstead Heath, in leafy north London, is proud of its walk-on part in the history of Marxism. It was here, on a Sunday, that Karl Marx would walk his family up Parliament Hill, reciting Shakespeare and Schiller along the way, for an afternoon of picnics and poetry. On a weekday, he would join his friend Friedrich Engels, who lived close by, for a brisk hike around the heath, where the "old Londoners", as they were known, mulled over the Paris Commune, the Second International and the nature of capitalism.

Today, on a side road leading off from the heath, the Marxist ambition remains alive in the house of Eric Hobsbawm. Born in 1917 (in Alexandria, under the British protectorate of Egypt), more than 20 years after both Marx and Engels had died, he knew neither man personally, of course. But talking to Eric in his airy front room, filled with family photos, academic honours and a lifetime of cultural objets, there is an almost tangible sense of connection to the men and their memory.

The last time I interviewed Eric, in 2002, his brilliant autobiography Interesting Times – chronicling a youth in Weimar Germany, a lifetime's love of jazz and his transformation of the study of history in Britain – had appeared to great acclaim. It was also amid another cyclical media attack, in the wake of Martin Amis's anti-Stalin book Koba the Dread, on Eric's membership of the Communist party. The "Marxist professor" of Daily Mail ire did not seek, as he put it, "agreement, approval or sympathy", but, rather, historical understanding for a 20th-century life shaped by the struggle against fascism.

Since then things have changed. The global crisis of capitalism, which has wreaked havoc on the world economy since 2007, has transformed the terms of debate.

Suddenly, Marx's critique of the instability of capitalism has enjoyed a resurgence. "He's back," screamed the Times in the autumn of 2008 as stock markets plunged, banks were summarily nationalised and President Sarkozy of France was photographed leafing through Das Kapital (the surging sales of which pushed it up the German bestseller lists). Even Pope Benedict XVI was moved to praise Marx's "great analytical skill". Marx, the great ogre of the 20th century, had been resuscitated across campuses, branch meetings and editorial offices.

So there seemed no better moment for Eric to bring together his most celebrated essays on Marx into a single volume, together with new material on Marxism in light of the crash. For Hobsbawm, the continual duty to engage with Marx and his multiple legacies (including, in this book, some fine new chapters on the meaning of Gramsci) remains compelling.

But Eric himself has changed. He suffered a nasty fall over Christmas and can no longer escape the physical constraints of his 93 years. But the humour and the hospitality of himself and his wife, Marlene, as well as the intellect, political incisiveness and breadth of vision, remain wonderfully undimmed. With a well-thumbed copy of the Financial Times on the coffee table, Eric moved seamlessly from the outgoing President Lula of Brazil's poll ratings to the ideological difficulties faced by the Communist party in West Bengal to the convulsions in Indonesia following the 1857 global crash. The global sensibility and lack of parochialism, always such a strength of his work, continue to shape his politics and history.

And after one hour of talking Marx, materialism and the continued struggle for human dignity in the face of free-market squalls, you leave Hobsbawm's Hampstead terrace – near the paths where Karl and Friedrich used to stroll – with the sense you have had a blistering tutorial with one of the great minds of the 20th century. And someone determined to keep a critical eye on the 21st.

Tristram Hunt At the heart of this book, is there a sense of vindication? That even if the solutions once offered by Karl Marx might no longer be relevant, he was asking the right questions about the nature of capitalism and that the capitalism that has emerged over the last 20 years was pretty much what Marx was thinking about in the 1840s?

Eric Hobsbawm Yes, there certainly is. The rediscovery of Marx in this period of capitalist crisis is because he predicted far more of the modern world than anyone else in 1848. That is, I think, what has drawn the attention of a number of new observers to his work – paradoxically, first among business people and business commentators rather than the left. I remember noticing this just around the time of the 150th anniversary of the publication of The Communist Manifesto, when not very many plans were being made for celebrating it on the left. I discovered to my amazement that the editors of the [in-flight] magazine of United Airlines said they wanted to have something about the Manifesto. Then, a bit later on, I was having lunch with [financier] George Soros, who asked: "What do you think of Marx?" Even though we don't agree on very much, he said to me: "There's definitely something to this man."

TH Do you get the sense that what people such as Soros partly liked about Marx was the way he describes so brilliantly the energy, iconoclasm and potential of capitalism? That that's the part that attracted the CEOs flying United Airlines?

EH I think that it is globalisation, the fact that he predicted globalisation, as one might say a universal globalisation, including the globalisation of tastes and all the rest of it, that impressed them. But I think the more intelligent ones also saw a theory that allowed for a sort of jagged development of crisis. Because the official theory in that period [the late 1990s] theoretically dismissed the possibility of a crisis.

TH And this was the language of "an end to boom and bust" and going beyond the business cycle?

EH Exactly. What happened from the 1970s on, first in the universities, in Chicago and elsewhere and, eventually, from 1980 with Thatcher and Reagan was, I suppose, a pathological deformation of the free-market principle behind capitalism: the pure market economy and rejection of state and public action that I don't think any economy in the 19th century actually practised, not even the USA. And it was in conflict with, among other things, the way in which capitalism had actually worked in its most successful era, between 1945 and the early 1970s.

TH By "successful", you mean in terms of raising living standards in the postwar years?

EH Successful in that it both made profits and ensured something like a politically stable and socially relatively contented population. It wasn't ideal, but it was, shall we say, capitalism with a human face.

TH And do you think that the renewed interest in Marx was also helped by the end of the Marxist/Leninist states. The Leninist shadow was taken away and you were able to return to the original nature of Marxian writing?

EH With the fall of the Soviet Union, the capitalists stopped being afraid and to that extent both they and we could actually look at the problem in a much more balanced way, less distorted by passion than before. But it was more the instability of this neoliberal globalised economy that I think began to become so noticeable at the end of the century. You see, in a sense, the globalised economy was effectively run by what one might call the global north-west [western Europe and North America] and they pushed forward this ultra-extreme market fundamentalism. Initially, it seemed to work quite well – at least in the old north-west – even though from the start, you could see that at the periphery of the global economy it created earthquakes, big earthquakes. In Latin America, there was a huge financial crisis in the early 1980s. In the early 1990s, in Russia, there was an economic catastrophe. And then towards the end of the century, there was this enormous, almost global, breakdown ranging from Russia to [South] Korea, Indonesia and Argentina. This began to make people think, I feel, that there was a basic instability in the system that they had previously dismissed.

TH There has been some suggestion to say that the crisis we've seen since 2008 in terms of America, Europe and Britain isn't so much a crisis of capitalism, per se, but of the modern west's finance capitalism. Meanwhile, Brazil, Russia, India and China – "Bric" – are growing their economies on increasingly capitalist models at the same time. Or is this simply our turn to suffer the crises they had 10 years ago?

EH The real rise of the Bric countries is something that has happened in the past 10 years, 15 years at most. So to that extent you can say that it was a crisis of capitalism. On the other hand, I think there's a risk in assuming, as neoliberals and free marketeers do, that there's only one type of capitalism. Capitalism is, if you like, a family, with a variety of possibilities, from the state-directed capitalism of France to the free-market of America. It's therefore a mistake to believe that the rise of the Bric countries is simply the same thing as the generalisation of western capitalism. It isn't: the only time they tried to import free-market fundamentalism wholesale was into Russia and there it became an absolutely tragic failure.

TH You raised the issue of the political consequences of the crash. In your book, you drop an insistence on looking at the classic texts of Marx as providing a coherent political programme for today, but where do you think Marxism as a political project goes now?

EH I don't believe that Marx ever had, as it were, a political project. Politically speaking, the specific Marxian programme was that the working class should form itself into a class-conscious body and act politically to gain power. Beyond that, Marx quite deliberately left it vague, because of his dislike of utopian things. Paradoxically, I would even say that the new parties were largely left to improvise, to do what they could do without any effective instructions. What Marx had written about simply amounted to little more than clause IV-style ideas about public ownership, nowhere actually near enough to provide a guidance to parties or ministers. My view is that the main model that 20th-century socialists and communists had in mind was the state-directed war economies of the first world war, which weren't particularly socialist but did provide some kind of guidance on how socialisation might work.

TH Are you not surprised by the failure of either a Marxian or a social democratic left to exploit the crisis of the last few years politically? We sit here some 20 years on from the demise of one of the parties you most admire, the Communist party in Italy. Are you depressed by the left's state at the moment in Europe and beyond?

EH Yes, of course. In fact, one of the things I'm trying to show in the book is that the crisis of Marxism is not only the crisis of the revolutionary branch of Marxism but in the social democratic branch too. The new situation in the new globalised economy eventually killed off not only Marxist-Leninism but also social democratic reformism – which was essentially the working class putting pressure on their nation states. But with globalisation, the capacity of the states to respond to this pressure effectively diminished. And so the left retreated to suggest: "Look, the capitalists are doing all right, all we need to do is let them make as much profit and see that we get our share."

That worked when part of that share took the form of creating welfare states, but from the 1970s on, this no longer worked and what you had to do then was, in effect, what Blair and Brown did: let them make as much money as possible and hope that enough of it will trickle down to make our people better off.

TH So there was that Faustian bargain that during the good times, if the profits were healthy and investment could be secured for education and health, we didn't ask too many questions?

EH Yes, so long as the standard of living improved.

TH And now with the profits falling away, we are struggling for answers?

EH Now that we're going the other way with western countries, where economic growth is relatively static, even declining, then the question of reforms becomes much more urgent again.

TH Do you see as part of the problem, in terms of the left, the end of a conscious and identifiable mass working class, which was traditionally essential to social democratic politics?

EH Historically, it is true. It was around the working-class parties that social democratic governments and reforms crystallised. These parties were never, or only rarely, completely working class. They were, to some extent, always alliances: alliances with certain kinds of liberal and leftwing intellectuals, with minorities, religious and cultural minorities, possibly many countries with different kinds of working, labouring poor. With the exception of the United States, the working class remained a massive, recognisable bloc for a long time – certainly well into the 1970s. I think the rapidity of deindustrialisation in this country has played hell with not only the size but also, if you like, the consciousness of the working class. And there is no country now in which the pure industrial working class in itself is sufficiently strong.

What is still possible is that the working class forms, as it were, the skeleton of broader movements of social change. A good example of this, on the left, is Brazil, which has a classic case of a late-19th-century Labour party based on an alliance of trade unions, workers, the general poor, intellectuals, ideologists and varying kinds of left [wingers], which has produced a remarkable governing coalition. And you can't say it's an unsuccessful one after eight years of government with an outgoing president on 80% approval ratings. Today, ideologically, I feel most at home in Latin America because it remains the one part of the world where people still talk and conduct their politics in the old language, in the 19th- and 20th-century language of socialism, communism and Marxism.

TH In terms of Marxist parties, something that comes out very strongly in your work is the role of intellectuals. Today, we see enormous excitement on campuses such as yours at Birkbeck, with meetings and rallies. And if we look at the works of Naomi Klein or David Harvey or the performances of Slavoj Zizek, there's real enthusiasm. Are you excited by these public intellectuals of Marxism today?

EH I'm not sure there has been a major shift, but there's no doubt: over the present government cuts there will be a radicalisation of students. That's one thing on the positive side. On the negative side… if you look at the last time of massive radicalisation of students in '68, it didn't amount to all that much. However, as I thought then and still think, it's better to have the young men and women feel that they're on the left than to have the young men and women feel that the only thing to do is to go and get a job at the stock exchange.

TH And do you think men such as Harvey and Zizek play a sort of helpful role in that?

EH I suppose Zizek is rightly described as a performer. He has this element of provocation that is very characteristic and does help to interest people, but I'm not certain that people who are reading Zizek are actually drawn very much nearer rethinking the problems of the left.

TH Let me move from west to east. One of the urgent questions you ask in this book is whether the Chinese Communist party can develop and respond to its new place on the global stage.

EH This is a big mystery. Communism's gone, but one important element of communism remains, certainly in Asia, namely the state Communist party directing society. How does this work? In China, there is, I think, a higher degree of consciousness of the potential instability of the situation. There is probably a tendency to provide more elbow room for a rapidly growing intellectual middle class and educated sectors of the population, which, after all, will be measured in tens, possibly hundreds of millions. It's also true that the Communist party in China appears to be recruiting a largely technocratic leadership.

But how you pull all this stuff together, I don't know. The one thing that I think is possible with this rapid industrialisation is the growth of labour movements, and to what extent the CCP can find room for labour organisations or whether they would regard these as unacceptable, in the way they regarded the Tiananmen Square demonstrations [as unacceptable], is unclear.

TH Let's talk about politics here in Britain, to get your sense of the coalition. It seems to me there's a 1930s air to it in terms of its fiscal orthodoxy, spending cuts, income inequalities, with David Cameron as an almost Stanley Baldwin figure. What is your reading of it?

EH Behind the various cuts being suggested, with the justification of getting rid of the deficit, there clearly seems to be a systematic, ideological demand for deconstructing, semi-privatising, the old arrangements – whether it's the pension system, welfare system, school system or even the health system. These things in most cases were not actually provided for either in the Conservative or the Liberal manifesto and yet, looking at it from the outside, this is a much more radically rightwing government than it looked at first sight.

TH And what do you think the response of the Labour party should be?

EH The Labour party on the whole has not been a very effective opposition since the election, partly because it spent months and months electing its new leader. I think the Labour party should, for one thing, stress much more that for most people in the past 13 years, the period was not one of collapse into chaos but actually one where the situation improved, and particularly in areas such as schools, hospitals and a variety of other cultural achievements – so the idea that somehow or other it all needs to be taken down and ground into the dust is not valid. I think we need to defend what most people think basically needs defending and that is the provision of some form of welfare from the cradle to the grave.

TH You knew Ralph Miliband, as the Miliband family are old friends. What do you think Ralph would have made of the contest between his sons and the outcome of Ed leading the party?

EH Well, as a father, he obviously couldn't help but be rather proud. He would certainly be much to the left of both of his sons. I think that Ralph was really identified for most of his life with dismissing the Labour party and the parliamentary route – and hoping that somehow it would be possible that a proper socialist party could come into being. When Ralph finally got reconciled to the Labour party, it was in the least useful period, namely in the Bennite period when it didn't really do much good. None the less, I think Ralph would certainly have hoped for something much more radical than his sons have so far looked like doing.

TH The title of your new book is How to Change the World. You write, in the final paragraph, that "the supersession of capitalism still sounds plausible to me". Is that hope undimmed and does that keep you working and writing and thinking today?

EH There's no such thing as undimmed hope these days. How to Change the World is an account of what Marxism fundamentally did in the 20th century, partly through the social democratic parties that weren't directly derived from Marx and other parties – Labour parties, workers' parties, and so on – that remain as government and potential government parties everywhere. And second, through the Russian Revolution and all its consequences.

The record of Karl Marx, an unarmed prophet inspiring major changes, is undeniable. I'm quite deliberately not saying that there are any equivalent prospects now. What I'm saying now is that the basic problems of the 21st century would require solutions that neither the pure market, nor pure liberal democracy can adequately deal with. And to that extent, a different combination, a different mix of public and private, of state action and control and freedom would have to be worked out.

What you will call that, I don't know. But it may well no longer be capitalism, certainly not in the sense in which we have known it in this country and the United States.