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The head of the UK's largest dairy farmers' co-operative has warned that prices may rise sharply in the event of a "no-deal" Brexit.

Arla is behind brands such as Cravendale Milk and Lurpak and imports about 15% of its products.

Its UK boss told the ´óÏó´«Ã½ that if the UK could not strike a free trade deal with the EU, tariffs could add as much as 30% to their prices.

A government spokesperson said it was working closely with the food industry.

After the Brexit transition period expires at the end of December, dairy goods are amongst those which could face the highest increase in such taxes.

In theory, that could add about 40p to the price of a pack of imported butter or mozzarella, if passed on to consumers in full.

Research commissioned by Arla, from the London School of Economics, claims that 40% in total of food and agricultural products used by British households and businesses come from the European Union (EU). The study calculated that without a deal, foods imported from the EU could face charges of nearly 18%.

Passing a free trade deal by 1 January would take away the risk of those tariffs. But the extra border checks and other formalities that would still apply could still raise costs for businesses, and potentially disrupt imports.

Arla's UK managing director, Ash Amirahmadi, said his organisation faced filling in an extra 30,000 pieces of paperwork from next year. He estimated that grappling with new measures could add as much as 10% to costs.

Describing his collective of 2,300 UK farmers as a "low margin business", he said they would have no choice but to pass on increased costs to retailers.

With supermarkets commonly having very low profit margins themselves, he was concerned that those prices might be passed on to shoppers.

And the cost of change could be more than financial. Mr Amirahmadi claimed dairy products are the way "many people get their essential nutrients....and we're very concerned if we have to increase our prices."

A government spokesman said: "The UK has a highly resilient food supply chain and there will not be an overall shortage of food, regardless of what trading arrangements we agree with the EU.

"We are in regular contact with the food industry to support its preparations for a range of scenarios, and will continue to work closely with them to ensure people across the country have the food and supplies they need."

But Mr Amirahmadi pointed out that it would take years, and more investment, before the industry could source solely from the UK.

"What we're looking for is for the government to support the industry and to enable us to be competitive on the world stage.

"That includes making sure we protect our standards on foods."