Retailers have warned that there will be shortages of fresh food coupled with potential price rises if there is a no-deal Brexit.

The body representing supermarkets and other chains told MPs that they could not understand why Michael Gove had claimed otherwise in a BBC interview over the weekend.

Fresh food travelling into the UK from the EU will not be subject to checks, but delays caused by checks on the French side could mean perishables such as tomatoes, lettuce, cabbage, cauliflower and cheese could all be hit by delays.

“It will affect fresh food in various ways, availability, shelf life and potentially cost,” said Andrew Opie, the director of food and sustainability of the British Retail Consortium.

“Our assessment is based on discussion with our members, who move fresh food every day, and the likely disruption [in Dover and Calais],” he told MPs on the Brexit select committee.

“We modelled that with our members who have told us there will be disruption to fresh food.”

He said the original March Brexit date was bad, but October was “probably the worst time to face a no-deal Brexit” with stockpiling capacity limited because warehouses would have long been booked up for Christmas stock.

“Logistics are already at full stretch, warehousing is at full premium,” he told MPs.

Opie said the consortium had warned the government and every MP of the risks as far back as January.

He also warned that there was a basic infrastructure problem, with a shortage of the heat-treated wooden pallets required by the EU to move fresh food across the border.

Asked if the government was stockpiling pallets, Opie said no, but they had been told that talks were under way with manufacturers to produce more.

The MPs said the French authorities had told them that truck drivers could be delayed for up to eight hours in Calais if they did not have the right paperwork.

The committee also heard that Calais and Eurotunnel ports would be “clogged up” in a no-deal Brexit, even in the best-case scenario.

Karen Wheeler, former head of Brexit border delivery at HMRC, said even if 80% of trucks got through the Dover and Folkestone to Calais routes by ferry or train, there would be an issue.

She said in June HMRC assessed that about 50% of trucks could turn up at the port without the correct paperwork for export.

She revealed that the French authorities had told HMRC that they “might hold those trucks for between two and eight hours” if they did not have the correct customs declarations documents.

Many small businesses “might still leave it to the wire to prepare” and would be caught out.

Applying for a special EORI number for exporting to the UK would take “two minutes” but the real issue was the customs declaration itself.

It was typically so complex that businesses hire a customs agent to help them deal with the thousands of commodity codes and rules of origin, Wheeler told MPs. “Not something that Joe Bloggs would normally be able to do.”

Even in the best case where there was no delay – with 70-80% of trucks getting through customs easily – “you would still get delays under those circumstances because 20% of the 10,000 trucks a day would still cause Calais and Eurotunnel to clog up,” she said.