Brits could turn back to cheddar if the price of French cheese shoots up after a no-deal Brexit.
Tesco's chair John Allan told the BBC that import taxes could push up the price of brie by as much as 40%.
He said it might "change the mix of what people eat", leading to people buying more British cheddar.
He added food bills could climb by 5% on average in the event of a no-deal Brexit, with some products increasing even more.
He warned consumers could face some disruption to supplies while the industry adjusted to the new situation next year.
Earlier, Mr Allen said the grocer had been stockpiling some non-fresh food as it prepares for potential shortages.
Last ditch trade talks between the UK and EU ended without agreement on Wednesday evening when Prime Minister Boris Johnson met in Brussels with European Commission President Ursula von der Leyen.
Time is running out to reach a deal before 31 December, when the UK stops following EU trading rules.
Mr Allen forecast that without a deal food inflation would climb between 3% and 5%, and "vastly more on some selected items".
Despite the impact on prices, he said consumers can expect "pretty much the same choice of products" on the shelves once Tesco had adjusted to the new set-up.
Mr Allan said Tesco was able to stockpile what he called "longer-life food", but there could be temporary shortages of "short-life fresh foods".
He told Bloomberg: "We are trying to ensure that we have stockpiled as much as we can of long-life products either in our own warehouses or with our suppliers."
Will food be more expensive after 1 January?
Under WTO rules, supermarkets and other importers would have to pay substantial tariffs on many foods they bring in from the EU.
Meat and dairy products face particularly high tariffs, but many other areas including fruit and vegetables would be also affected.
As an extreme case, the London School of Economics estimates that some speciality cheeses such as halloumi and roquefort could be 55% more expensive.
(Tariffs don't just apply to food - cars made in the EU, for instance, would attract a 10% tariff. But food and drinks are the area where the highest tariffs apply.)
Government minister George Eustice said prices on average would rise less than 2%, although he admitted some items such as pork and beef would be hit harder.
In the short term, shops could absorb those extra costs themselves. But in the longer term they would likely pass some or all of that cost on to customers, in the form of higher prices.
Earlier on Wednesday, the government announced a series of measures to address urgent concerns about the operation of trade between Northern Ireland and the rest of the UK.
With a couple of rare exceptions, all goods going from UK to Northern Ireland will be exempt from EU tariffs. Proposed food safety checks on goods entering NI will be waived for a grace period of three months.
Mr Allen said three months was better than nothing and a "a step in the right direction".
Brexit - The basics
- Brexit happened but rules didn't change at once: The UK left the European Union on 31 January 2020, but leaders needed time to negotiate a deal for life afterwards - they got 11 months.
- Talks are happening: The UK and the EU have until 31 December 2020 to agree a trade deal as well as other things, such as fishing rights.
- If there is no deal: Border checks and taxes will be introduced for goods travelling between the UK and the EU. But deal or no deal, we will still see changes.
Tesco has also been diverting shipments to ports other than Dover, which he described as "the throat that gets squeezed".
It comes as ports such as Felixstowe and Southampton face severe delays caused by a surge in imports, leading some to warn that soaring freight costs could be passed on to UK consumers.
On Wednesday, trade group Logistics UK blamed the disruption on concerns about a no-deal Brexit, as well as Covid and the Christmas rush.
Mr Allan cautioned against altering UK food regulations after Brexit, telling the BBC that food suppliers had "no wish to deviate from current food standards".
He spoke out against allowing imports of US chlorine-washed chicken, saying: "I think most of the food industry is opposed to it."
He added: "I can't see us being enthusiastic about contributing to anything that would lower food standards in the UK."
Like other supermarkets, Tesco has seen its profits surge in the pandemic as people spend more time at home and splash out on food.
Last week, the retailer said it would repay £585m in business rates relief after it was criticised for paying dividends to shareholders.
Other retailers followed suit, including Asda, Morrisons and Sainsbury's.