The government may be stockpiling medicines but the Brexit secretary, Dominic Raab, has promised consumers there will be no shortage of ingredients for the bacon, lettuce and tomato sandwich in the event the UK crashes out of the EU.

But Britain’s leading bacon supplier, the owner of Danepak, warned that while there may not be shortages, the price of the BLT might go up as the vast majority of rashers come from the EU and could be hit by tariffs.

Raab made his remarks to rebut recent claims by the British Sandwich Association there could be a shortage of fresh food in the event of the UK crashing out of the UK.

“Who is credibly suggesting in a no-deal scenario the EU would not want to sell food to UK consumers? Let me assure you that, contrary to one of the wilder claims, you will still be able to enjoy a BLT after Brexit,” said Raab.

But Lars Albertsen, the vice-president for global exports at Danish Crown, which owns Danepak and three pig abattoirs in the UK, pointed out: “There is definitely a risk that the bacon will get more expensive if there is no deal.”

The EU tariff on non-EU bacon is about €68 to the kilo. Britain may have to pay an extra 15p on the price of a pack of eight rashers.

Danish Crown said neither Raab, nor any bacon supplier, could definitively say what would happen to bacon supplies as the “price will be decided by the market” and the availability of pork which ebbs and flows according to farming conditions like other foodstuffs.

The prospect of a “sandwich famine” referred to by Raab comes as anxiety grows over Britain’s declining self-sufficiency in food which has left the country producing about 60% of what it eats.

Nearly all the ingredients in the BLT are likely to be imported. Britain imports 10 times as much bacon as it exports and 50% more butter than it exports. Tomatoes are likely to come from the Netherlands and lettuce from Spain, Poland or even the US which started to supply greens last month because of a British shortage in the heatwave.

Raab did not address the basis of this concern – the delays due to customs and phytosanitary checks post Brexit.

The Eurotunnel owner, Getlink, and Calais port owners have been warning for a year that a no-deal Brexit could mean fresh fruit and vegetables including lettuce and tomatoes rotting on the roadside if Calais or Dover become lorry parks.

Albertsen sought to assure the British consumer: “Whatever happens, Danish Crown will continue to export to the UK as it has for the past 130 years. It has survived two world wars, the cold war, the great depression, the financial crisis of the last decade. We are pretty sure Danish bacon will survive Brexit.”

• This article was amended on 24 August 2018 to clarify that the UK imports 50% more butter than it exports.

