In the wake of an ocean of writing linking Brexit to the zeitgeisty Dunkirk spirit, here’s one more martial metaphor. Self-evidently, this is the phoney war stage of the process. Negotiations have barely started; the prime minister is on holiday. Most importantly, the fragile tangle of threads that defines what passes for Britain’s economic wellbeing – that mixture of affordable essentials, freely available credit and dependable house prices which ensures no one gets too uppity about stagnating wages – just about remains intact. Meanwhile, ministers – and Labour politicians – talk about the fundamentals of leaving the European Union as if we can push Brussels in any direction we fancy and freely choose no end of measures to ease our passage out.

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The recent noise about freedom of movement is a case in point. If the government has a coherent position, it seems to be that migration from the EU under current rules will end in 2019, but also carry on, with – according to the home secretary, anyway – the proviso that during an “implementation phase” of up to four years, people from the EU will simply have to add their names to a national register. Thus, a great human army which keeps so much of Britain’s economy ticking over will still be available, just as long as the right arrangements are put in place.

This is, of course, somewhat less than credible, as evidenced by a mounting crisis that has yet to turn critical but is bubbling away across the country. At the very least, we are fundamentally changing the basis on which people can live and work in the UK, swapping residence as a right for a much more uncertain system dependent on political caprice.

If you wanted to be more dramatic, you might say that the 2016 European referendum in effect put a huge neon sign over Britain, saying, “Foreigners not welcome”. And to make matters worse, the value of sterling is making coming here even less attractive.

“The perception from overseas is we are xenophobic, we’re racist, and the pound has plummeted too. We’ve gone with Brexit and that makes us look unfriendly.” Those are the words of John Hardman, director of Hops Labour Solutions, which supplies about 12,000 workers a year to food-growers. He reckons that when it comes to “food-picking jobs in agriculture – which means everything from strawberries to brussels sprouts”, there is currently a Brexit-related shortfall of about 20%, which chimes with recent surveys by the National Farmers Union.

What of the much-discussed prospect of food rotting in the fields? “We’re not far off. I suspect that’ll definitely happen next year,” he says. Hardman reckons that growers are beginning to question their investment plans for 2018, fearing crops going unpicked, and says that large-scale growers might soon consider moving into central and eastern Europe, at which point those much-fetishised union jacks will start to disappear from strawberry punnets.

According to a study by the GMB union sourced from official figures, nearly half the workers employed in the UK’s fruit and vegetable “processing and preserving sector” are from countries within the EU. In meat processing, the figure is 44%. But among seasonal businesses that use fruit and veg pickers, the number usually rockets to more than 90%. Such figures denote thousands of people who are often poorly paid and prepared to do monotonous, frequently back-breaking work, thereby keeping a large swath of Britain’s food economy ticking over.

But not for much longer, perhaps. In the latest survey by the Association of Labour Providers, 30% of agencies who supply workers to British food and agriculture businesses say they don’t expect to be able to source sufficient workers for the remainder of this summer’s peak picking period, and almost half say they will have problems in the busiest period before Christmas. One industry insider talks anxiously about a “real and escalating issue”, and echoes huge concerns about the lack of basic understanding among ministers. Others refer to factors beyond Brexit that are convincing would-be migrant workers to look elsewhere: the revived fortunes of the eurozone economies and an equally impressive picture in such eastern European countries as Poland and Hungary, for instance.

Whenever the subject of free movement and the UK’s food industry comes up, many people envisage a Brexit in which wages will leap up, British workers will return to the fields, and all will be well. Superficially, the fact that 40% of labour providers in agriculture and food say the businesses they service have recently had to increase wages makes it look like things might be pointing in that direction. But the food sector is just as complex and fragile as the rest of the economy, and it may not take much to tip it into chaos.

Supermarkets can sell cheap food to people who haven’t had a pay rise in years thanks to an industry partly built around growing and packing businesses that tend to run on unbelievably tight margins (half of British fruit farms are reckoned to turn profits of less than 2% of turnover). But in the main food-growing areas of England – the East Anglian fens, for instance – unemployment rates tend to be low. And even leave-voting locals acknowledge that, whatever the wage rates (if you’re up for the work, you can turn £10 to £15 an hour picking strawberries), most UK-born people wouldn’t be interested in the kind of jobs that might soon be available.

Besides, seeing Brexit as any kind of dependable cure for low-wage work is surely a political category error. The project that Britain is embroiled in is not a great progressive drive to right social wrongs: it is an emotion-driven revolution led by people on the political right who evidently have no idea what they are doing. And sooner or later, thanks to a combination of reduced domestic production and insufficient workers, Brexit may well explode into further increases in food prices – a prospect which takes us back into the fragilities of Britain’s teetering economic model: limited household budgets, rising debt, and the fact that what separates millions on limited incomes from borderline starvation is the availability of cut-price food.

Meanwhile, the most zealous Brexiteers look forward to a supremely unlikely future in which we spurn the huge amount of food we import from Europe and somehow either produce our own, or fly in stuff from around the globe. Beyond the prospect of stupidly increased food miles and basic fruit and veg suddenly refrigerated to within an inch of its life and transported across time zones, such half-baked visions may well bump up against one big problem: the effects of Brexit (including the loss of farming subsidies, which is a whole other mess) meaning we may not have much of a British food industry left – a strange thing to be embraced by self-styled patriots, but there we are.

Who knows? We could turn the suddenly vacated fields into nostalgic theme parks, where people could watch re-enactments of the second world war while eating imported strawberries: it would be the perfect Brexit day out, should anyone be able to afford it.

• John Harris is a Guardian columnist