Autumn Statement 2016: Inflation
A woman shops at a Sainsbury's store in London Neil Hall/ Reuters

The former chief of executive of Sainsbury's has warned British shoppers are "completely in the dark" about the impact Brexit will have on their weekly shop, but they would almost certainly face higher prices.

Speaking to BBC Panorama, Justin King, who ran the FTSE 100-listed group for a decade, said it was very clear shoppers would face "higher prices, less choice and poorer quality".

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Membership of the European Union guarantees free trade across the continent, which has so far helped British retailer to keep food prices down. However, the pound's sharp devaluation since the Brexit vote and the rising inflation could soon see costs head in the opposite direction.

The former Sainsbury's CEO, who supported the 'Remain' campaign in the lead up to last year's referendum, added the "last thing" supermarkets would do was to reveal plans to hike prices in the future.

"Brexit, almost in whatever version it is, will introduce barriers," he said.

"That makes it less efficient which means all three of those benefits - prices, quality and choice - go backwards."

He added being part of the EU had allowed British consumers to have access to out-of-season vegetables and fruits all year round, while allowing retailers to secure deals with the best producers on the continent.

King, who left the retailer in 2014, added food had to be put on the Brexit agenda "pretty soon", as Britain has less than two years to reach an agreement with the EU.

"There has been, in my estimation, almost no conversation about the potential impact of Brexit on the food supply chain by definition," he said.

However, John Mills, chairman of consumer goods firm JML claimed prices were kept artificially high by the EU.

"Food prices inside the EU vary from food product to food product, but the average is something like 20% higher than they are in the rest of the world - so there is very substantial scope for food prices coming down if we switch sources of supply outside the EU," he said.

"The reason why food prices are higher inside the EU is because they have got tariffs which keep the prices up.

"It's not anything to do with quality - it's due to the institutional arrangements which means the food prices are kept much higher to increase farmers' incomes."