BREXITEERS said that leaving the EU would lead Britain to a land flowing with milk and honey. But as worries of a no-deal Brexit mount, the country is instead talking of hoarding emergency rations. Google searches for the word “stockpile” have jumped in the past week, approaching the all-time high seen shortly after the referendum of June 2016.

Some countries could just about cope if their borders were closed to imports, at least in the short term. Britain is not one of them. Imports and exports are worth over 60% of British GDP, twice America’s level. Half of Britain’s food comes from abroad, most passing through EU ports.

The Brexit secretary has promised, not entirely reassuringly, that there will be “adequate food” whatever happens; the health secretary has said the NHS is preparing to stockpile medicine. Yet it is not clear that enough is being done to honour these pledges. Britain spends some £50bn ($66bn) a year on medicine and non-perishable food from the EU. So stocking up with enough for just a month would cost around £4bn—more than the entire no-deal planning budget of £3bn set aside in November. Nor is there any sign that reserves are being built up. Food and medicine imports have been steady in recent months.

Companies, many of whose manufacturing methods rely on raw materials and components zipping between production facilities in different countries, are also talking about stockpiling. Airbus says it has asked its suppliers to start “ramping up” their stock of components for its aeroplanes. Pharmaceutical firms including AstraZeneca, Novartis and Sanofi have said that they will increase their inventories.

Yet the hoarders seem to be in the minority. Take JJ Churchill, a supplier of turbine blades to the aviation industry. The firm held a board meeting on July 31st to discuss whether to stockpile parts, and decided against, as it would tie up too much working capital. Andrew Churchill, the executive chairman, argues that the fog of Brexit makes it unclear which parts are vulnerable to disruption.

Economy-wide data reveal little evidence of firms preparing for “no deal”. Firms’ stocks of inventories are, if anything, falling. Our analysis of over 5,000 categories of goods shows that imports of parts, raw materials and machinery—“capital” and “intermediate” goods, in the jargon—are in fact declining. That is consistent with a nervousness about the future, though of a different sort. It could suggest that bosses are worried about the strength of demand after Brexit, and may therefore be trimming investment in future production.

If Brexit day approaches with no deal in sight, companies and the government may decide that stockpiling is unavoidable. At that point they would face a problem: a shortage of warehousing. Vacancy rates are already low, thanks in part to the expansion of e-tailers such as Amazon. And stockpiling would require a huge amount of space. Britain guzzles 3bn litres of imported booze every year. A month’s supply would be enough to fill 100 Olympic-sized swimming pools. Better start digging.