The puzzlement is understandable. Fifteen years ago, after the collapse of communism in Eastern Europe, there appeared to be a general assumption that Marx was now an ex-parrot. He had kicked the bucket, shuffled off his mortal coil and been buried forever under the rubble of the Berlin Wall. No one need think about him - still less read him - ever again.
'What we are witnessing,' Francis Fukuyama proclaimed at the end of the Cold War, 'is not just the ... passing of a particular period of postwar history, but the end of history as such: that is, the end point of mankind's ideological evolution.'
But history soon returned with a vengeance. By August 1998, economic meltdown in Russia, currency collapses in Asia and market panic around the world prompted the Financial Times to wonder if we had moved 'from the triumph of global capitalism to its crisis in barely a decade'. The article was headlined 'Das Kapital Revisited'.
Even those who gained most from the system began to question its viability. The billionaire speculator George Soros now warns that the herd instinct of capital-owners such as himself must be controlled before they trample everyone else underfoot. 'Marx and Engels gave a very good analysis of the capitalist system 150 years ago, better in some ways, I must say, than the equilibrium theory of classical economics,' he writes. 'The main reason why their dire predictions did not come true was because of countervailing political interventions in democratic countries. Unfortunately we are once again in danger of drawing the wrong conclusions from the lessons of history. This time the danger comes not from communism but from market fundamentalism.'
In October 1997 the business correspondent of the New Yorker, John Cassidy, reported a conversation with an investment banker. 'The longer I spend on Wall Street, the more convinced I am that Marx was right,' the financier said. 'I am absolutely convinced that Marx's approach is the best way to look at capitalism.' His curiosity aroused, Cassidy read Marx for the first time. He found 'riveting passages about globalisation, inequality, political corruption, monopolisation, technical progress, the decline of high culture, and the enervating nature of modern existence - issues that economists are now confronting anew, sometimes without realising that they are walking in Marx's footsteps'.
Quoting the famous slogan coined by James Carville for Bill Clinton's presidential campaign in 1992 ('It's the economy, stupid'), Cassidy pointed out that 'Marx's own term for this theory was "the materialist conception of history", and it is now so widely accepted that analysts of all political views use it, like Carville, without any attribution.'
Like Molière's bourgeois gentleman who discovered to his amazement that for more than 40 years he had been speaking prose without knowing it, much of the Western bourgeoisie absorbed Marx's ideas without ever noticing. It was a belated reading of Marx in the 1990s that inspired the financial journalist James Buchan to write his brilliant study Frozen Desire: An Inquiry into the Meaning of Money (1997).
'Everybody I know now believes that their attitudes are to an extent a creation of their material circumstances,' he wrote, 'and that changes in the ways things are produced profoundly affect the affairs of humanity even outside the workshop or factory. It is largely through Marx, rather than political economy, that those notions have come down to us.'
Even the Economist journalists John Micklethwait and Adrian Wooldridge, eager cheerleaders for turbo-capitalism, acknowledge the debt. 'As a prophet of socialism Marx may be kaput,' they wrote in A Future Perfect: The Challenge and Hidden Promise of Globalisation (2000), 'but as a prophet of the "universal interdependence of nations" as he called globalisation, he can still seem startlingly relevant.' Their greatest fear was that 'the more successful globalisation becomes the more it seems to whip up its own backlash' - or, as Marx himself said, that modern industry produces its own gravediggers.
The bourgeoisie has not died. But nor has Marx: his errors or unfulfilled prophecies about capitalism are eclipsed and transcended by the piercing accuracy with which he revealed the nature of the beast. 'Constant revolutionising of production, uninterrupted disturbance of all social conditions, everlasting uncertainty and agitation distinguish the bourgeois epoch from all earlier ones,' he wrote in The Communist Manifesto.
Until quite recently most people in this country seemed to stay in the same job or institution throughout their working lives - but who does so now? As Marx put it: 'All that is solid melts into air.'
In his other great masterpiece, Das Kapital, he showed how all that is truly human becomes congealed into inanimate objects - commodities - which then acquire tremendous power and vigour, tyrannising the people who produce them.
The result of this week's BBC poll suggests that Marx's portrayal of the forces that govern our lives - and of the instability, alienation and exploitation they produce - still resonates, and can still bring the world into focus. Far from being buried under the rubble of the Berlin Wall, he may only now be emerging in his true significance. For all the anguished, uncomprehending howls from the right-wing press, Karl Marx could yet become the most influential thinker of the 21st century.
· Francis Wheen's acclaimed biography Karl Marx is published by Fourth Estate