The US ambassador to the UK has dismissed criticism of US food standards as a “marketing campaign” after a former minister said a post-Brexit trade deal could not accept “woefully deficient” American farming practices.

Woody Johnson, who last week accused the EU of being a “museum of agriculture”, said Donald Trump would make sure any trade deal between the UK and US “has to include farming and farm products”.

“The president has made it pretty clear he would love to have a robust trade deal with the UK. But any trade deal that we do with the UK will have to include agriculture. Agriculture is extremely important to the president,” he told the BBC’s Radio 4 Today programme.

Johnson caused an outcry when he invited the UK to drop its opposition to certain practices such as the use of hormones in beef and chlorine washes for chicken when considering a trade deal.

In response, George Eustice, a Brexit supporter who until last week was the minister for agriculture, said the US should join the back of a queue for a post-Brexit trade deal if it thought its “backward” animal welfare and food safety standards would be accepted in Britain.

Signing any deal that allowed a loosening of food standards would be a mistake because it could give free trade a bad name, he said.

Challenged about Eustice’s comments, Johnson said “a lot of these statements are designed perhaps by the EU to create barriers” and that “the campaign against US farm products has been very, very successful”.

He wrongly claimed that the US had the lowest level of food poisoning. British rates are in fact better than those in America, according to the Sustain alliance for better food and farming.

The issue is a contentious one within the UK government. The environment secretary, Michael Gove, has insisted food and welfare standards will be maintained, but the trade secretary, Liam Fox has defended the safety of chlorine-washed chicken.

Writing for the Guardian, Eustice said the UK had a sophisticated and discerning market for food, but agriculture in the US “remains quite backward in many respects”.

“Their livestock sectors often suffer from poor husbandry which leads to more prevalence of disease and a greater reliance on the use of antibiotics,” he said. “Whereas we have a ‘farm to fork’ approach to managing disease and contamination risk throughout the supply chain through good husbandry, the culture in the US is more inclined to simply treat contamination of their meat at the end with a chlorine or similar wash.”

He said the situation in relation to animal welfare was even worse. “Legislation as regards animal welfare is woefully deficient,” he said. “There are some regulations governing slaughterhouses but they are not as comprehensive as ours. As far as on-farm welfare legislation is concerned, there is virtually nothing at all at a federal level and only very weak and patchy animal welfare regulations at a state level, predominantly in the west coast states.

“There is a general resistance to even acknowledging the existence of sentience in farm animals, which is quite extraordinary.”

Eustice said he was strongly supportive of the UK striking trade deals after Brexit, but they should demand that suppliers meet British standards. He highlighted a Conservative manifesto commitment to do so.

“If the Americans want to be granted privileged access to the UK market, then they will have to learn to abide by British law and British standards, or they can kiss goodbye to any trade deal and join the back of the queue,” he said.

He said trade deals should be an opportunity to “project British values of kindness and compassion” rather than allowing them to be undermined.