Campbell reckons global peak production of conventional oil - the kind associated with gushing oil wells - is approaching fast, perhaps even next year. His calculations are based on historical and present production data, published reserves and discoveries of companies and governments, estimates of reserves lodged with the US Securities and Exchange Commission, speeches by oil chiefs and a deep knowledge of how the industry works.

"About 944bn barrels of oil has so far been extracted, some 764bn remains extractable in known fields, or reserves, and a further 142bn of reserves are classed as 'yet-to-find', meaning what oil is expected to be discovered. If this is so, then the overall oil peak arrives next year," he says.

If he is correct, then global oil production can be expected to decline steadily at about 2-3% a year, the cost of everything from travel, heating, agriculture, trade, and anything made of plastic rises. And the scramble to control oil resources intensifies. As one US analyst said this week: "Just kiss your lifestyle goodbye."

But the Campbell analysis is way off the much more optimistic official figures. The US Geological Survey (USGS) states that reserves in 2000 (its latest figures) of recoverable oil were about three trillion barrels and that peak production will not come for about 30 years. The International Energy Agency (IEA) believes that oil will peak between "2013 and 2037" and Saudi Arabia, Kuwait, Iraq and Iran, four countries with much of the world's known reserves, report little if any depletion of reserves. Meanwhile, the oil companies - which do not make public estimates of their own "peak oil" - say there is no shortage of oil and gas for the long term. "The world holds enough proved reserves for 40 years of supply and at least 60 years of gas supply at current consumption rates," said BP this week.

Indeed, almost every year for 150 years, the oil industry has produced more than it did the year before, and predictions of oil running out or peaking have always been proved wrong. Today, the industry is producing about 83m barrels a day, with big new fields in Azerbaijan, Angola, Algeria, the deep waters of the Gulf of Mexico and elsewhere soon expected on stream.

But the business of estimating oil reserves is contentious and political. According to Campbell, companies seldom report their true findings for commercial reasons, and governments - which own 90% of the reserves - often lie. Most official figures, he says, are grossly unreliable: "Estimating reserves is a scientific business. There is a range of uncertainty but it is not impossible to get a good idea of what a field contains. Reporting [reserves], however, is a political act."

According to Campbell and other oil industry sources, the two most widely used estimates of world oil reserves, drawn up by the Oil and Gas Journal and the BP Statistical Review, both rely on reserve estimates provided to them by governments and industry and do not question their accuracy.

Companies, says Campbell, "under-report their new discoveries to comply with strict US stock exchange rules, but then revise them upwards over time", partly to boost their share prices with "good news" results. "I do not think that I ever told the truth about the size of a prospect. That was not the game we were in," he says. "As we were competing for funds with other subsidiaries around the world, we had to exaggerate."

Most serious of all, he and other oil depletion analysts and petroleum geologists, most of whom have been in the industry for years, accuse the US of using questionable statistical probability models to calculate global reserves and Opec countries of drastically revising upwards their reserves in the 1980s.

"The estimates for the Opec countries were systematically exaggerated in the late 1980s to win a greater slice of the allocation cake. Middle East official reserves jumped 43% in just three years despite no new major finds," he says.

The study of "peak oil" - the point at which half the total oil known to have existed in a field or a country has been consumed, beyond which extraction goes into irreversible decline - used to be back-of-the envelope guesswork. It was not taken seriously by business or governments, mainly because oil has always been cheap and plentiful.

In the wake of the Iraq war, the rapid economic rise of China, global warming and recent record oil prices, the debate has shifted from "if" there is a global peak to "when".

The US government knows that conventional oil is running out fast. According to a report on oil shales and unconventional oil supplies prepared by the US office of petroleum reserves last year, "world oil reserves are being depleted three times as fast as they are being discovered. Oil is being produced from past discoveries, but the re­serves are not being fully replaced. Remaining oil reserves of individual oil companies must continue to shrink. The disparity between increasing production and declining discoveries can only have one outcome: a practical supply limit will be reached and future supply to meet conventional oil demand will not be available."

It continues: "Although there is no agreement about the date that world oil production will peak, forecasts presented by USGS geologist Les Magoon, the Oil and Gas Journal, and others expect the peak will occur between 2003 and 2020. What is notable ... is that none extend beyond the year 2020, suggesting that the world may be facing shortfalls much sooner than expected."

According to Bill Powers, editor of the Canadian Energy Viewpoint investment journal, there is a growing belief among geologists who study world oil supply that production "is soon headed into an irreversible decline ... The US government does not want to admit the reality of the situation. Dr Campbell's thesis, and those of others like him, are becoming the mainstream."

In the absence of reliable official figures, geologists and analysts are turning to the grandfather of oil depletion analysis, M King Hubbert, a Shell geologist who in 1956 showed mathematically that exploitation of any oilfield follows a predictable "bell curve" trend, which is slow to take off, rises steeply, flattens and then descends again steeply. The biggest and easiest exploited oilfields were always found early in the history of exploration, while smaller ones were developed as production from the big fields declined. He accurately predicted that US domestic oil production would peak around 1970, 40 years after the period of peak discovery around 1930.

Many oil analysts now take the "Hubbert peak" model seriously, and the USGS, national and oil company figures with a large dose of salt. Similar patterns of peak discovery and production have been found throughout all the world's main oilfields. The first North Sea discovery was in 1969, discoveries peaked in 1973 and the UK passed its production peak in 1999. The British portion of the basin is now in serious decline and the Norwegian sector has levelled off.

Other analysts are also questioning afresh the oil companies' data. US Wall street energy group Herold last month compared the stated reserves of the world's leading oil companies with their quoted discoveries, and production levels. Herold predicts that the seven largest will all begin seeing production declines within four years. Deutsche Bank analysts report that global oil production will peak in 2014.

According to Chris Skrebowski, editor of Petroleum Review, a monthly magazine published by the Energy Institute in London, conventional oil reserves are now declining about 4-6% a year worldwide. He says 18 large oil-producing countries, including Britain, and 32 smaller ones, have declining production; and he expects Denmark, Malaysia, Brunei, China, Mexico and India all to reach their peak in the next few years.

"We should be worried. Time is short and we are not even at the point where we admit we have a problem," Skrebowski says. "Governments are always excessively optimistic. The problem is that the peak, which I think is 2008, is tomorrow in planning terms."

On the other hand, Equatorial Guinea, Sao Tome, Chad and Angola are are all expected to grow strongly.

What is agreed is that world oil demand is surging. The International Energy Agency, which collates national figures and predicts demand, says developing countries could push demand up 47% to 121m barrels a day by 2030, and that oil companies and oil-producing nations must spend about $100bn a year to develop new supplies to keep pace.

According to the IEA, demand rose faster in 2004 than in any year since 1976. China's oil consumption, which accounted for a third of extra global demand last year, grew 17% and is expected to double over 15 years to more than 10m barrels a day - half the US's present demand. India's consumption is expected to rise by nearly 30% in the next five years. If world demand continues to grow at 2% a year, then almost 160m barrels a day will need to be extracted in 2035, twice as much as today.

That, say most geologists is almost inconceivable. According to industry consultants IHS Energy, 90% of all known reserves are now in production, suggesting that few major discoveries remain to be made. Shell says its reserves fell last year because it only found enough oil to replace 15-25 % of what the company produced. BP told the US stock exchange that it replaced only 89% of its production in 2004.

Moreover, oil supply is increasingly limited to a few giant fields, with 10% of all production coming from just four fields and 80% from fields discovered before 1970. Even finding a field the size of Ghawar in Saudi Arabia, by far the world's largest and said to have another 125bn barrels, would only meet world demand for about 10 years.

"All the major discoveries were in the 1960s, since when they have been declining gradually over time, give or take the occasional spike and trough," says Campbell. "The whole world has now been seismically searched and picked over. Geological knowledge has improved enormously in the past 30 years and it is almost inconceivable now that major fields remain to be found."

He accepts there may be a big field or two left in Russia, and more in Africa, but these would have little bearing on world supplies. Unconventional deposits like tar sands and shale may only slow the production decline.

"The first half of the oil age now closes," says Campbell. "It lasted 150 years and saw the rapid expansion of industry, transport, trade, agriculture and financial capital, allowing the population to expand six-fold. The second half now dawns, and will be marked by the decline of oil and all that depends on it, including financial capital."

So did the Swiss bankers comprehend the seriousness of the situation when he talked to them? "There is no company on the stock exchange that doesn't make a tacit assumption about the availability of energy," says Campbell. "It is almost impossible for bankers to accept it. It is so out of their mindset."

Crude alternatives

"Unconventional" petroleum reserves, which are not included in some totals of reserves, include:

Heavy oils

These can be pumped just like conventional petroleum except that they are much thicker, more polluting, and require more extensive refining. They are found in more than 30 countries, but about 90% of estimated reserves are in the Orinoco "heavy oil belt" of Venezuela, which has an estimated 1.2 trillion barrels. About one third of the oil is potentially recoverable using current technology.

Tar sands

These are found in sedimentary rocks and must be dug out and crushed in giant opencast mines. But it takes five to 10 times the energy, area and water to mine, process and upgrade the tars that it does to process conventional oil. The Athabasca deposits in Alberta, Canada are the world's largest resource, with estimated reserves of 1.8 trillion barrels, of which about 280-300bn barrels may be recoverable. Production now accounts for about 20% of Canada's oil supply.

Oil shales

These are seen as the US government's energy stopgap. They exist in large quantities in ecologically sensitive parts of Colorado, Wyoming and Utah at varying depths, but the industrial process needed to extract the oil demands hot water, making it much more expensive and less energy-efficient than conventional oil. The mining operation is extremely damaging to the environment. Shell, Exxon, ChevronTexaco and other oil companies are investing billions of dollars in this expensive oil production method.