On the outskirts of Heathrow there is a multistorey warehouse that plays a remarkable role in the eating habits of millions of people. The British Airways perishables handling centre is the arrival point for 90,000 tonnes of airfreighted fresh produce a year: everything from chopped melon and pineapple fruit salads to baby sweetcorn and asparagus. Every day these once exotic items arrive in the belly of passenger jets from Africa and Asia, destined for the chilled aisles of supermarkets such as Marks & Spencer.

Only not at the moment. With almost all air travel grounded due to volcanic ash, the freight operator that runs the perishables centre today declared things "at a standstill". By definition, these perishable imports do not store well, and Waitrose is already warning of potential shortages. Rather than weigh down the aircraft with unnecessary skin and pips, much of the fruit is pre-sliced in African facilities, making retailers even less able to create contingency buffers. Our desire for all-year-round oral gratification has left us perilously dependent on just-in-time supply chains in the stratosphere.

But fruit and veg is only one aspect of our dependence on air travel revealed by this week's surprise volcanic disruption. Courier companies such as FedEx and DHL have had to shut down their services, disrupting delicate logistic chains across industry. As anyone who has ordered an iPod from Apple knows, it is possible to track in real time the flow of high-value electronics flown across the world by these companies. Or at least, it is normally.

Iceland's revenge on the world economy has given us a glimpse of a world without air travel. We are used to images of stranded passengers – marooned by terrorism, industrial action or perhaps just our overcrowded and underinvested aviation industry. But it is very rare for the skies to be scoured so comprehensively as this. As many people observed yesterday, the sight of clear blue skies without a contrail to be seen was strangely uplifting.

But it also had a post-apocalyptic feel about it, more reminiscent of a Hollywood disaster movie than environmental utopia.

The short-term economic cost is likely to be minimal. Airlines will lose a few tens of millions of pounds each from the disruption – hardly ideal at a time of big losses and falling passenger numbers, but probably not catastrophic in the long term.

The larger numbers bandied about by so-called experts about the cost to the economy at large should be taken with a pinch of salt. Not only is it impossible to quantify disruption on such a diverse scale, but much economic activity is merely postponed by such events rather than eliminated entirely.

More important is the psychological impact of such events. The terrorist attacks of 11 September forced many companies to re-examine the resilience of their supply chains – but that was nearly a decade ago now, and the continued march of globalisation will have left many of them vulnerable. Climate change should force business to think more about the alternatives, but it rarely does. Greens should also celebrate this timely reminder of what the world might look like when the oil runs out.

Sadly, if the stratosphere clears over Britain tomorrow, we will probably have forgotten all this by next weekend when we start booking our summer holidays or planning the fruit salad for that spring picnic.

But just imagine what Europe might look like in six months time, or six years time, if the volcano were to continue belching out ash on a scale that made air travel permanently unviable.