John Vidal's report on US diplomatic cables from Saudi Arabia raises the spectre of premature peak oil: an unexpected deline in global oil production in an oil-dependent world. The US government is among many administrations that routinely reassure the public that supplies of oil can go on growing far into the future. But in private, top diplomats have been telling Washington that they hold deep concerns about supplies from the world's number one supplier. This is an issue that has far-reaching consequences for an oil-importing nation like the UK, and for the global economy.

The latest batch of leaked cables report the views of Sadad al-Husseini, a former board member of the national oil company Saudi Aramco and a geologist who headed exploration and production for the company from 1986 to 2004. He and the US consul-general met in November 2007, when Saudi Aramco were halfway through a $50bn investment programme aiming to lift Saudi maximum daily production capacity from 9.5 million barrels a day to 12.5m by 2009.

Al-Husseini told the Americans he believed that the 12.5m barrel a day target would prove impossible. The kingdom might get to 12m barrels a day given 10 years, but before then – perhaps as early as 2012 – global production would have hit the highest level it ever will, and given that demand won't be abating by then given levels of economic growth in China and India, the oil price will soar. He told the Americans plainly that the Saudis will not be able to ride to the rescue: the Saudi oil industry was overstating its recoverable reserves so as to spur foreign investment, he alleged, at the same time as it was badly underestimating the time needed for bringing new oil on tap.

By 2009, the Saudis were producing 9.7m barrels a day, and claiming more than 4m barrels of spare capacity: capacity beyond the daily production level that can be opened up in an effort to "swing produce" – that is to say, flood the market with oil and bring the price down. Many oil analysts question this figure, and the cables suggest there is good reason to for such scepticism.

Al-Husseini's gloomy view is known from public interviews such as the one he gave to the US Association for the Study of Peak Oil. What is interesting in the cables is the American diplomats' reaction to his view. "Al-Husseini is no doomsday theorist," the cable concludes. "His pedigree, experience and outlook demand that his predictions be thoughtfully considered."

Seven months later, in a June 2008 cable, they went further. "Our mission now questions how much the Saudis can now substantively influence the crude markets over the long term. Clearly they can drive prices up, but we question whether they any longer have the power to drive prices down for a prolonged period."

No US government official has come close to saying this in public. It is a conclusion of profound significance for the world economy, if correct.

So is it correct? Al-Husseini told the Americans in October 2007 that he didn't think there were enough qualified staff or contracting companies available to Saudis to meet their targets. . In a September 2007 cable the embassy reports hearing "constant complaints of shortages of materials, qualified workers, and infrastructure." Such was the desperation that workers were being hired who had fraudulent documentation. The June 2008 cable reports major project delays and accidents as "evidence that the Saudi Aramco is having to run harder to stay in place – to replace the decline in existing production."

After this graphic warning about the difficulties the Saudis are having even to replace existing production, much less grow it, the cable goes on to say "while this mission is far from embracing doomsday 'peak oil' theorists, Saudi Aramco's challenges are significant." Al-Husseini himself insisted to embassy staff that he "does not subscribe to the theory of peak oil", before going on to air precisely the concerns that advocates of premature peak oil do: that global demand has essentially met supply, and that a premature drop in global oil production lies a worryingly short way off.

Peak oil is not a "theory." Because oil is a finite resource, it is an inevitability. The debate is all about its timing. Al-Husseini is quoted in the 2007 cable as believing that beyond maximum possible global oil production lies a plateau of production lasting perhaps 15 years. Many others who have "pedigree and experience" think there will be a drop in production within just a few years, and we are in danger of that drop being so steep as to merit description as a collapse. In the YouTube interview al-Husseini recorded in 2009 he talks of a shortage of capacity withing just two to three years – by 2011, conceivably. He then says: "in the long term it's even worse."

The peak oil debate – whether one uses the "P" word or not – involves huge stakes. If US diplomats based in Saudi Arabia harbour fears that the Saudis can't produce enough oil to head off ruinous oil prices, then they are merely telling the US government what a spectrum of UK industry is already telling the UK government. We are asleep at the wheel here: choosing to ignore a threat to the global economy that is quite as bad as the credit crunch, and quite possibly worse.

• Jeremy Leggett is the founder and chairman of Solarcentury, the UK's largest solar solutions company.