Asking about "prehistoric man" is difficult, because this encompasses a huge variety of situations and almost all of human history. However, I'll assume you are mainly talking about hunting and gathering societies most specifically when you say "prehistoric man" which I can answer somewhat.

Generally we know from modern hunter-gatherers that these types of societies usually produce the majority of their daily caloric intake from vegetable matter. For instance, the mongongo nut provides most of the caloric intake for the !Kung people of the Kalahari desert. Generally, women and children are going to be the ones gathering fruit, nuts, roots, and other vegetable matter for the group while the men of the group are usually the hunters who range farther from camp to hunt larger game. Children can also help the women with some gathering activities, and both women and children can hunt actively for smaller game in the vicinity of camp such as rabbits or turtles. Granted, if a woman is out and about gathering and sees a deer or the like, she probably wont let it just walk away even if she isn't actively looking for prey like that.

So basically, the answer to your question is that when hunter gatherers eat meat is based largely on when the men in the group can actually hunt and kill something. Some parts of the year or in certain locations this may be a lot easier than others, and so meat might be very available depending on where and when the group is hunting. This is why gathering is so important, because it provides a steady and reliable supply of calories even if the men fail to find something that day.

There are exceptions of course. Most societies living in the arctic circle (even up to the present) can't rely on plant foods for most or even any part of the year and make very heavy use of animal meat and fat (especially the fat) as part of their diet. Reindeer, caribou, seals, fish, and whaling are all part of the daily diet. Likewise, groups living during the last ice age (the Pleistocene) in Europe and North America might have relied more heavily on megafauna (so mammoths and other large animals) as part of their diet. However, I suspect some of this might just be a figment of the archaeological record since the only things that generally preserve from these times periods are stone weapons and the bones of large animals. Even then, the amount of mammoth bone at pleistocene sites in the Americas is vastly outnumbered by the amount of turtle remains found at these sites, which suggests a lot more reliance on women and vegetable products/small animals for daily living.

In short, hunter-gatherer groups for the most part (ignoring the arctic circle and some other situations) will eat meat whenever it is available which can be very seasonally and location dependent. Hunter might only bring in a kill once or week or less, or they could bring in something every day. Most groups supplement this hunted protein intake by "gathering" turtles, rabbits, and other small animals to add more daily or semi-daily protein to the diet.

As for Medieval man, that I can't answer.

Also consider /r/AskAnthropology.

There've been a couple all right answers but I don't think they've taken ecology into account enough. Rather than thinking strictly about how much of the diet is meat versus how much is plants, you need to look at what proportions of the food available in the environment is animal vs. plant based.

Groups like the Hadza and Ju/'hoansi ("!Kung") live in subtropical semi-arid savanna environments. These environments can support a high proportion of tasty mammalian biomass. However, though semi-arid savannas have lower plant productivity than, say, temperate or tropical forests, a higher proportion of that productivity is edible roots, fruits, and seeds. Because of this, the Hadza and Ju/'hoansi use a lot of plants in their diet. However, tropical forest foragers, such as the Ache, Asian Negritos, and African pygmies, eat much more meat, even though edible animal biomass is lower in tropical forests, because the high plant productivity of tropical forests is mostly tied up in wood and inedible leaves.

Taiga and arctic foragers also relied heavily on meat because taiga and tundra don't provide much in the way of plant food, and what edible plants there are tend to be sweet fruits, which, while important in the diet, can't be a staple.

Additionally, there's plenty of maritime and riverine foragers who rely on "meat" in the form of fish and shellfish.

So: it's highly variable and there's not one way that foragers live, but if you look worldwide, meat tends to be more important to foragers than plant foods.

(this is taken almost entirely from The Foraging Spectrum by Robert Kelly, a really great introduction if you're interested in hunter-gatherers)

However, through most of our species' history in the Pleistocene in Africa, we inhabited dryer savanna environments, so from the origin of our species around 200,000 years ago to the Out-of-Africa migrations 60-50,000 years ago, we probably did eat mostly plants.