Leading retail bosses, including the chief executives of Sainsbury’s, Asda, Marks & Spencer, the Co-op and Waitrose, have written to the government warning of significant disruption to food supplies in the event of a no-deal Brexit.

The letter, backed by the British Retail Consortium trade body, also warns that grocery prices are likely to rise, as nearly a third of the food eaten in Britain comes from the EU and would be subject to import tariffs if the UK exits without a trade deal in place.

“We are extremely concerned that our customers will be among the first to experience the realities of a no-deal Brexit,” said the letter, which is signed by the BRC and 10 leading store chain bosses.

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“We anticipate significant risks to maintaining the choice, quality and durability of food that our customers have come to expect in our stores, and there will be inevitable pressure on food prices from higher transport costs, currency devaluation and tariffs.”

The letter comes before another crucial day in parliament on Tuesday, as MPs vote on a series of amendments to Theresa May’s Brexit plan.

The retailers expressed particular concern about fresh foods, saying it is impossible to stockpile produce such as salad and fruit.

The bosses – who include the Sainsbury’s chief executive, Mike Coupe; the Asda chief executive, Roger Burnley; and the Marks & Spencer CEO, Steve Rowe; as well as the heads of the Co-op, Waitrose, Costcutter, KFC UK, Pret a Manger, Lidl and McDonald’s – said retailers typically store no more than two weeks’ stock.

They said that “as prudent businesses” they are stockpiling in order to be prepared for no deal but with frozen and chilled storages nearing capacity, there is very little general warehousing space available in the UK.

“While we have been working closely with our suppliers on contingency plans, it is not possible to mitigate all the risks to our supply chains and we fear significant disruption in the short-term as a result if there is no Brexit deal,” the letter said.

The store bosses warned of “major disruption” at Calais, a key route for food imports to the UK, potentially reducing freight trade by nearly 90%, as the French government has said it will enforce sanitary and customs checks on exports from the EU, which will cause long delays.

“For consumers, this will reduce the availability and shelf life of many products in our stores,” the letter said.

The retail analysts GlobalData said food price inflation could rise to about 5.1%, from 2.4%, in the case of a no-deal Brexit.

“There has simply not been enough information provided by the government on how food prices, availability and regulations will be affected in the event of a no-deal Brexit. The just-in-time supply chain that UK supermarkets operate on means that there is not the specialist infrastructure in place to deal with stockpiling – particularly of fresh goods,” said Thomas Brereton, an analyst at GlobalData.

“While the supermarkets are currently engaged in price wars – somewhat driven by the exceedingly successful proposition of the discounters Aldi and Lidl – it will be difficult for retailers to stop prices shooting upwards if import costs rise as much as speculated.”

Downing Street said ministers were taking special measures to minimise the impact of a no-deal Brexit on supermarkets’ suppliers and insisted that food was not going to run out as a result.

“The government has well-established ways of working with the food industry to prevent disruption and we are using these to support preparations for leaving the European Union,” the prime minister’s spokesman said.

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The spokesman said extra freight capacity would be made available to alleviate any pressure on the Dover-Calais crossing “to ensure vital goods continue to come into the country” but would not say what constituted vital goods, other than potentially medical supplies.

No 10 also promised there would be a “functioning customs, excise and VAT system” on day one if there was a no-deal Brexit and special measures to ensure traffic is able to flow on the M20 route to the channel ports.

However, the Food and Drink Federation, which represents thousands of food processors and manufacturers, has said a no-deal Brexit would be a “catastrophe”, with uncertainty undermining investment and constraining businesses’ ability to plan and export.

The letter emerged after the British Chambers of Commerce said that thousands of the firms it represented had already triggered contingency plans for a no-deal Brexit, including proposals to move operations out of the UK.