But the sceptics are fighting back. Britain's Economic and Social Research Council (ESRC) is conducting 19 separate projects at a cost of well over pounds 2m to discover the secrets of the "Asian miracle". And the view so far of the research programme director, Gerald Segal? "There will be no such thing as the Pacific Century."
In the next issue of Prospect magazine, Dr Segal lists the "half-truths and dubious assumptions" behind what he calls "Pacific-chic". Not only is the idea of a "Pacific Century" not new, he points out - it was first touted in the middle of the 19th century by a US secretary of state, William Seward, who thought east Asia would dominate the 20th century - but Dr Segal disputes whether there is something usefully described as "the Pacific", remarking that London is closer to any major city in east Asia than is any major North American city.
Nor is there any political or cultural unity across Asia: "The inhabitants of Asia have never been a single unit and have never defined themselves as part of a single entity. Their self-consciousness as 'Asia' or 'East Asia' was given to them by Europeans."
Dr Segal is swimming against a strong tide. Prominent politicians of all shades argue that lessons must be drawn from Asian success. On a recent visit to Singapore, Tony Blair was impressed by the way forced savings are invested in infrastructure, while Chris Patten, a possible future Tory leader, says his experience as Governor of Hong Kong has convinced him that the state must shrink to create room for economic growth.
David Howell, chairman of the Commons select committee on foreign affairs, writes of "the coming fact of Asian dominance" in a paper published by the Demos think-tank. For the first time in centuries, he argues, "the issue is not Westernisation but Easternisation".
Predicting that millions of people in parts of Asia will shortly be living at standards "higher than their European counterparts, in superior physical surroundings", he says: "Asia may actually be leading the world in moral as well as economic terms, and ... tomorrow's ideas may well be found there already in practice".
Dr Segal, however, argues that, if "Asia" does not exist, neither do "Asian values". "Yes, many East Asians do work hard, save a great deal and care about family and education," he writes. "So did the Victorians or those supposed to be infused with a Protestant work ethic." Even the notion that there is an east Asian "economic miracle" is a myth, he adds.
One of the main proponents of this view is Paul Krugman, professor of economics at Stanford University in the US, who has pointed out that the West was just as alarmed at the explosive growth of the Soviet Union in the 1950s and early 1960s as it is now at the rise of east Asia. In 1957, one eminent economist concluded that "a collectivist, authoritarian state" was probably better at achieving economic growth than free-market democracies, and calculated that the Soviet economy might outstrip that of the US by the early 1970s.
Apart from Japan, the countries of east Asia, like the postwar Soviet Union, are booming because of mammoth investment rather than any growth in efficiency, says Professor Krugman, who calls it "perspiration, not inspiration". Nobody is suggesting that east Asia is performing as inefficiently as the old Soviet regime, but there is agreement that the "tigers" will grow more slowly as their economies mature. That is already happening in Japan, where growth has lagged behind Britain's in each of the past four years.
The new scepticism appears to have been absorbed by Mr Patten, who said in London last week that there was no need to fall back on "divine intervention" to explain Asia's economic transformation. "It has happened before," he said. "The pace of change is now very much faster, but the mechanics of change are very much the same." Asian economies would have to achieve "quality growth" to keep pace with Western Europe and North America, let alone catch up with them.
Messrs Patten, Howell and Segal all agree on one thing, however: with nearly half of all Japanese direct investment in Europe, and other east Asians following Japan's example, Britain is better placed than its European partners to take advantage of the region's growth. Whether or not there is any magic in the rise of the Asian tigers, they hope some of it will rub off on the British lion.