The incident occurred Monday afternoon as Michael Porter, 66, of Edinburgh accompanied his brother, John, 72, and sister-in-law, Mary, 77, as they walked their dog in Turleigh, Wiltshire, the Sun reported.
Porter's chest was crushed, while his brother suffered broken ribs and a collapsed lung. Mary Porter was not injured.
Porter had been a senior lecturer at the Center for Population Health Sciences at Edinburgh University.
There had been earlier incidents in the same field in 2008 and 2011, police said.
Minette Batters, who farms at Downton in Wiltshire, said dogs and cattle are not a good mix in the spring.
"Cows that are calving will always try to protect their young, and dogs often cause a problem," Batters told the Sun.