Food prices will rise unless the government ensures EU citizens can work in the UK after Brexit, according to industry groups representing the major supermarkets and food manufacturers, including the owner of Marmite.

The open letter to the government is signed by 30 food and drink industry bodies, including the Food and Drink Federation, which represents major suppliers, including Marmite maker Unilever and Mr Kipling owner Premier foods; the British Retail Consortium, which counts Tesco, Sainsbury’s, Asda and Morrisons among its members, and the National Farmers Union.

The letter, published in the Guardian, says: “Workers from the European Union, some of whom are already leaving the UK, play a significant role in delivering affordable and high-quality food and drink.” It says they provide “an essential reservoir of skilled, semi-skilled and unskilled labour.”

Any points-based permit system for immigrants should place the food and drink supply chain on a par with financial services and the automotive sector, the industry leaders say. “All options should be explored, including a workable points-based system for shortage occupations, sector-based and seasonal/guest worker schemes and effective transitionary arrangements. If it is not, the UK will face less food choice and higher food prices.”

The letter, which is also signed by the heads of the British Beer & Pubs Association, the British Growers Association and the British Soft Drinks Association, claims that some EU workers have already begun to leave the UK in the wake of the Brexit vote which has led to a fall in the value of the pound. “The government can address this issue directly. It should offer unambiguous reassurance to EU workers throughout our supply chain about their right to remain here,” it said.

Employment agencies have warned that the UK’s food industry is facing the worst labour shortage for at least 12 years.

The Association of Labour Providers (ALP), whose employment agency members supply 70% of the temporary labour used by the food and drink industry, recently said responses to job ads had slumped by up to 70% as workers from the EU – who account for 90% of jobs in the sector – avoid coming to the UK.

The NFU has said farmers have seen a shortfall in EU workers, exacerbated by the drop in the pound against the euro, which has diminished the value of the money they are sending home.

Nearly 4 million people are employed in growing, harvesting, producing, packaging, selling and serving food and drink in the UK, a large proportion of whom are EU nationals.

Although food prices continue to fall amid heavy competition between the major supermarket chains and fast-growing discounters Aldi and Lidl, rising costs are expected to drive up inflation in the coming months.

A string of major food brands have sought increased cost prices from supermarkets as the fall in the pound has driven up the cost of importing ingredients and other essentials, such as packaging.

Unilever, which also owns Ben & Jerry’s and Dove; Typhoo; Birds Eye and Walkers are embroiled in an industry-wide battle over price increases caused by the 15% drop in the value of the pound against the euro and 18% against the dollar since the UK voted to leave the European Union.

The lower value of the pound is also expected to increase exports, potentially making it harder for UK companies to source home-grown ingredients. For example, the price of British butter has soared 80%, partly because processors have found exporting easier.

Food and drink is the UK’s biggest export, worth £18bn, led by Scotch whisky, chocolate, beer and salmon. Despite its relatively low profile, food manufacturing is worth more to the UK economy than the automotive and aerospace sectors combined.