Mesolithic people were hunter gatherers and I think, the effort expended on trapping and butchering larger animals probably exceeded their food value. Small animals and seafoods were found extensively in their diets but cooking methods were primitive so most of their food was plant based.
The Neolithic was characterised by the introduction of arable farming and domestication of animals so again I think their diet was again mainly plant based.
As a child, even in a comfortably off home, we only had meat at our main meal, and not always even then I can remember quite a number of meat free main meals in my mothers repertoire, cheese potato pie, baked beans, fried onion, boiled potatoes and gravy. Breakfast was usually something on toast and tea was bread, spread and one slice of cake.
When I started cooking 4ozs was a standard portion per person for meat ,but now I do not even do that much as I cook mainly casseroles and similar dishes and tend to pack them with lots of vegetables, so without consciously intending it the portion of meat per serving has fallen.