An hour before dawn, Britain’s largest food wholesaler is already winding down. New Covent Garden Market has been supplying London restaurants with fruit and vegetables from this sprawling depot in south London since the UK joined the Common Market in the mid-70s. A foodie revolution during the intervening four decades demands that ever fresher and more exotic produce is on the road before the sun starts to rise.

For those who have to fill the lorries, there is a new worry. As with many sectors, the food industry is trying to work out how it will cope if it is separated from its European supply chain by Brexit. The same ingredients of travel, trade and tourism that transformed the national palate could now turn sour, driving up prices and possibly sending us back to the days of curly sandwiches and limp lettuce.

“When I grew up, it was all pork chop, mash and peas,” says Nathan Humphries, a veteran salesman for an importer called the French Garden. “Now there’s all sorts of beautiful stuff,” he adds, waving to a cornucopia that runs from pink garlic to white peaches; yellow beans to greengages. After weeks of cold, wet weather in Britain, the greengages deliver a surprise jolt of sunshine from south-west France, sweet with juice and memories of foreign holidays.

At this time of year, the market is groaning with local produce, too. The first apples have started arriving from Kent. British cherries and sweetcorn are piled defiantly in union jack-festooned boxes. But most of the people who picked them are from eastern Europe. Behind the market’s third-generation cockney frontmen, the warehouses are also full of foreign-born packers and drivers. An estimated 25% of chefs and 70% of waiters in the restaurants the produce is heading for are EU nationals, according to a report by KPMG for the British Hospitality Association. The tables rely on 34 million foreign visitors.

Yellow beans … for which British consumers can thank trade with the EU. Photograph: Alamy

Asking whether Brexit will have an impact on British food can feel a bit like the Monty Python sketch that questioned what the Romans ever did for us. Few doubt the stakes are high. One academic report accused the government of “sleepwalking” into food insecurity. When bad Spanish weather caused a shortage of courgettes and lettuce last February, many saw it as a taste of the homegrown disruption to come.

Even in August, a country that grows just 15% of its own fruit and 55% of its vegetables cannot afford to cut the continental umbilical cord. The greengages arrived overnight from Rungis wholesale market in Paris, tunnelling under the Channel before fanning out across Britain in a delicate supply chain. Salads come from Spain in the winter; the Netherlands in spring and autumn. The port of Rotterdam is the year-round gateway for tropical imports.

But is this age of plenty really that fragile? Will the food revolution simply grind to a halt when Britain leaves the European Union? The government hopes to strike ambitious trade and customs deals to keep the goods flowing freely. EU citizens already working here in farms and restaurants will probably be allowed to stay – if they can be persuaded to. Some suspect Brexit has become Fleet Street’s new “millennium bug”: a reliable source of horror stories about a technical switchover that may yet pass largely unnoticed.

“There are ways and means,” says Damian Fowler, another New Covent Garden wholesaler who depends on frictionless access to the Channel tunnel. “The potential is there for [Brexit] to cause a problem, but we are quite a resourceful industry, and money is the greatest fertiliser ever.”

The government has published two policy papers outlining how it intends to prevent border delays and tariffs from obstructing the free flow of food to and from the EU. “We are absolutely determined to get a good Brexit deal for our food and farming sector,” says the Department for Environment, Food and Rural Affairs. “Leaving the EU provides us with a golden opportunity to better support our farmers to grow more, sell more and export more great British food, while continuing tariff-free trade for all our goods.”

Prawns … the British love exotic foreign varieties, but are less keen on the – very similar – local types. Photograph: Alamy

So far, much of the political focus has been on these opportunities for exporters, rather than potential headaches for importers or consumers. The Department for International Trade says it is time to start selling more “high-quality innovative British jams and marmalades” to countries such as France.

For producers such as Wilkin & Sons of Tiptree, in Essex, this is not a novel idea. It has been exporting to 60 countries since 1885. It is rather proud of its greengages, which it says are more subtle than “floury” French rivals.

But there is a catch. Growing 25 varieties of fruit in the English countryside is a labour-intensive business and the company’s managing director, Chris Newenham, is worried about how he will replace his seasonal workforce of 330 Bulgarian and Romanian pickers after Brexit. “We will continue, and find a way,” he says, pointing out that migrant labour schemes have been in place for fruit pickers since the 50s. But the nervousness is acute.

For EU farm workers, the uncertainty of their long-term future in the UK is compounded this year by a collapse in the value of the earnings they are able to send to families back home. One Bulgarian farm worker, who asked not to be named, said the fall of the pound to an eight-year low against the euro, meant they were working as hard as ever on this year’s harvest, but for 25% less money.

Some hope that robots will provide a solution to Brexit-induced labour shortages on farms, but Newenham is sceptical. “We are still at least 10 years away from a reliable robotic harvesting system,” he says. Even then, this might work for tabletop strawberry production, but will do little for Tiptree’s more exotic wonders, such as the medlar – a fruit so stubborn that it needs to rot, or “blet”, a little in the frost before it is ready for eating.

Although British people may not be keen to take over fruit-picking duties, they are partial to the fruits of plentiful foreign labour. Consumption of soft fruit in the UK has shot up over the last 20 years, according to an industry report. Today, we eat two-and-a-half times more strawberries and raspberries than in 1996, mostly homegrown. Without EU labour, we would be forced to import from Dutch and Belgian strawberry-growers or Portuguese raspberry-farmers, sending the price of a punnet soaring by an estimated 50%, and making the elusive five-a-day target even more distant for many.

Supermarkets are reluctant to talk about what may happen, referring questions to trade bodies instead. They were badly burned by “Marmite wars” at the outset of the Brexit process, when suppliers temporarily forced the much-loved British staple from shelves because retailers had refused to pass on soaring import costs after the referendum. Further product disruption could put these household names on the frontline of any political backlash.

One challenge for those who dream of British self-sufficiency is that what the country chooses to eat rarely matches up with what it is good at producing. The fishing industry, for example, is often singled out as a clearcut beneficiary of Brexit because of its ability to reclaim British fishing waters once we leave the Common Fisheries Policy. Yet most of the oily fish and shellfish caught in British waters are exported to the continent, while we would almost certainly continue to import white fish from non-EU countries such as Iceland and Norway.

British cherries … the vast majority are picked by EU workers. Photograph: Alamy

Andrew Kuyk, a former civil servant who now lobbies for the fishing industry in his role as director general of the Provision Trade Federation, charts the disconnect back to the “cod wars” in the 70s, which left British trawlers exiled from the Icelandic waters that once shaped national eating habits. But snobbery about traditional working-class seaside staples plays a part, too, as does ignorance over how to treat the delicacies that are shipped off to the continent. “We will happily eat prawns farmed in Thailand, but we turn our nose up at biologically similar prawns from the Irish coast,” says Kuyk. “The skill set you need to prepare and cook these more obscure fish species has long since gone.”

Most agree that Brexit does offer a potential opportunity to fix some of the wrongs of British food culture. A rediscovery of locally sourced produce could compensate for economic harm elsewhere, while at the same time reducing food miles and perhaps addressing the sometimes appalling labour standards that have marred the industry at home and abroad. But industry insiders are sceptical of the relentlessly upmarket vision presented by the environment secretary, Michael Gove.

“There is a seductive argument that the way forward is for us to be at the niche end of the market, with high animal and environmental standards,” says Kuyk. “But the heroic assumption is that consumers will be willing to pay for that. Some will, but some won’t be able to and will simply go back to cheap and cheerful instead. We can’t live on Duchy Originals alone.”

A different vision is peddled by the more ardent free-traders in the Conservative party. They see Brexit as an opportunity to shake off meddlesome food regulations and strike tariff-free trade deals, with cheaper importers. Only the leanest farmers will survive, but the resultant fall in consumer prices will ensure capital flows to more productive sectors of the economy instead.

Such thinking is regarded with horror among food producers, but it also spells a very different future for Britain’s food consumers. “In the long run, you might see the arrival of a different sort of food culture: served by automated picking and packing and much more mechanised manufacturing,” says Ian Wright of the Food and Drink Federation. “It’s difficult to believe all of that can be done and retain the food culture we currently have.”

Fresh peaches … a taste of foreign holidays. Photograph: Alamy

To chart a path through these two dystopian visions, perhaps the only way to preserve the relative abundance of both high-quality and cheap food that Britain enjoys today is to try to replicate as much of the single market as the EU will let us. “If we want the same choices at the same price points, then we have to have an EU/UK free-trade deal in place by March 2019. It’s the bedrock of much of the food culture we have,” says Wright.

“Any delay in fresh fruit and vegetables has a massive impact,” he adds, warning of the crippling impact of any customs or transport holdups. “People don’t understand the distribution miracle. Most fresh food arrives at the point of sale on the morning that it is sold and, as we saw with the iceberg lettuce shortage in February, it only takes a break in supply, be it weather or whatever, and you see those products wiped out within two or three days.”

Nonetheless, regulation and customs problems are small potatoes compared with the possible impact of labour shortages on the British tastebuds. While farmers may still have access to some seasonal workers – if the government can keep them out of the immigration statistics – the situation for restaurants is rather more acute.

“I don’t think it would be overstating it to say that Brexit could be catastrophic for our industry,” says Ufi Ibrahim, the chief executive of the British Hospitality Association. “If you don’t have a chef, you have no business. It’s immediate.”

Predicting a wave of restaurant and hotel closures if workers cannot be found, Ibrahim describes a similar polarisation of British eating culture to that predicted by the food producers: cheap and cheerful or luxury, but little in between. Labour shortages can be overcome only “if you can command very high volumes – Nando’s, McDonald’s, Costa – or if you are very high end,” she says. “Everything in the middle: the business model cannot be sustained. If [Brexit] happens as a cliff edge it will be catastrophic. There will be mass closures and consolidation and what you will be able to obtain in terms of choice and quality will fall.”

Higher prices, fewer outlets, lower quality and a more mechanised food culture is not a notion that Brexiters are likely to want to write on the side of a bus. Many importers are already coping with soaring input costs as a result of the weakened pound. Consumers fear the prospect of US-style deregulation – from hormone-treated beef and crops to chlorine-treated chicken – if Britain pursues trade deals at any costs. Such fears are rejected by Gove and the government, but those who have studied the policy conundrum are scathing about the myths that are peddled instead.

“Churchillian romantics who see Brexit as an opportunity to relive imperial or wartime days go silent if the culinary era of tinned peaches and spam is mentioned,” says Tim Lang, a professor of food policy at City university. “It was Europeanisation which coincided with – and, arguably, facilitated – the flowering of modern UK culinary culture.”

New Covent Garden Market … will its supply chain cope with Brexit? Photograph: Graeme Robertson/The Guardian

Such gloomy views of Brexit’s potential are not shared by all. Lindsey Bareham is a food writer whose book The Prawn Cocktail Years helped rediscover recipes that went out of fashion when the food revolution swept in. Where British food once suffered a cultural inferiority complex in relation to French and Italian cuisine, she believes the renaissance shows a country finally confident in its own taste.

“The fact we are going to leave the EU is not going to dampen our love of food, and cooking and eating out,” says Bareham. “We are becoming more like other European cultures that embrace food as part of a lifestyle. It’s not just fuel.”

That is certainly true down at New Covent Garden, where the latest hot import from the continent is micro-cress, Dutch plant seedlings that pack flavours such as aniseed and honey into tiny leaves. Another new delicacy from the same greenhouse is a flower bud called the szechuan button, which sends a startling electric buzz through the mouth and is apparently great in cocktails. Innovations such as these rely on a high-end London restaurant scene that could be hit by any number of Brexit-related obstacles.

But for wholesalers, such as Richard Harris of IA Harris & Sons, it is the loss of foreign workers across the food chain that could keep them awake all night. “It’s in my blood, but the next generation doesn’t seem so keen,” he says. “All the growers and pickers [in England] are foreign. [Brexit] could make wages here go ridiculous, and everything has to be passed on. That’s very scary from my point of view.”