I don't know about medieval times, but a lack of animal products in the diet of the the impoverished and imprisoned was a problem as recently as the early 1900s. The disease Pellagra[1] is caused by a lack of niacin in the diet, which can be commonly found in animal products (and certain plant products like legumes). It was considered a paupers disease and was most commonly found in rural areas and in the poor, imprisoned, or orphaned. The prevailing theory was that it was related to eating corn - either an insect born illness or a contaminant - when in reality it was a lack of diet diversity in the people who could only afford to eat corn. The history on Dr. Goldberger is actually really interesting and I recommend a skim of his Wikipedia page.

[1] https://en.m.wikipedia.org/wiki/Pellagra#History