Farmers told the royal couple that possible 40% tariffs on sheep, combined with a loss of European Union subsidies for farmers would bring about a "perfect storm".
Sam Rawling, a sheep farmer, said he was very surprised to see his industry voting for Brexit. "They have got to do other things to survive".
Adam Day, managing director of the Farming Network, said: "The worst case scenario post-Brexit is absolutely dire".
When he was asked by William how he felt about the future, he said: "Quite apprehensive at the moment. I wouldn't want to be the last generation after 500 years", of operating the family farm. "A lot of farming is an export market".
Later in the day, Kate and William joined the Cumbria Wildlife Trust and children from Patterdale School for an environmental educational session on the Ullswater Way.
"I came in my pants and my coat because I'm going to see some sheep", Middleton says in response.
The Duchess of Cambridge revealed that she'd brought her children to the Lake District during Prince George's half-term, and that "it was raining a lot and was a long way from their home in Norfolk, but they love it here", according to another person in the crowd.More news: Kevin Durant Listed As Questionable For Game 5
More news: Mexico Tariffs Are Still Possible
More news: Pelicans Provide Framework For Anthony Davis Trade Package
Upon arrival, Their Royal Highnesses met two young sisters who presented them with flowers.
The string of engagements comes just days after Kate, William and the rest of the extended royal family celebrated the Queen's birthday at the Trooping of the Colour. After all, the couple owns an English cocker spaniel named Lupo, whom Kate referenced during the visit.
"I know. I'm sorry", she said.
Mr Irving, 54, suffered a devastating auto crash in 2006, but overcame severe depression by walking his neighbour's dog Max before he adopted him.
Middleton, accompanied by husband Prince William, visited a farm in Cumbria, England, on Tuesday.
The couple met with members of the volunteer local mountain rescue team, first responders in the community, and organisations that are making good use with donations given by the Cumbria Community Foundation.