Absolutely. Hunting for food has been something that the English lower classes have traditionally done to the extent they could, but were often prevented from doing. There’s a reason that poachers are often rural folk heroes.
Here in the US, there never were Royal Forests — indeed, the very word “forest,” which was originally borrowed into English from French to describe aristocratic game preserves, is for us simply a term meaning woodland, particularly if large. Hunting (especially large game) often requires a license, but this can be pretty cheap — based on a bit of poking around, it appears that in Michigan, a base license (which lets you hunt small game, and is also a prerequisite most of the other licenses) is $11 for a state resident, and deer licenses are $20 per deer, both for bucks and for does. I’m told that in some Southern states, doe tags can be as little as $5 each, as I referenced above.
AFAICT, the low end of realistic yields from an adult deer is about 35 pounds of boneless lean meat, and substantially higher is easily possible. So even buying only a single deer tag (here in Michigan), not shooting any small game, and shooting a relatively small deer, you’re still looking at less than $1 per pound.
Relatedly, I’ve been told that the word “hunting” actually means something different in the US and the UK, specifically that in the UK, it implies “on horseback, with dogs,” and generally for foxes (which are never eaten, correct?). Here, mounted hunting with dogs is rare even in the states that permit it, and so “going hunting” by default means “with a gun,” or, more rarely “with a (cross)bow,” and usually for animals that one intends to eat at least the tastier portions of. Dogs are sometimes used to track, flush, or tree various animals (birds, raccoons, boar, etc.), but the kill is still made with a bow or a firearm, and 44% of American households own one or more dogs (more in rural areas).
My impression is that there are types of hunting that have “wealthy recreation” associations here, even apart from English-style horse-and-dog fox hunts. Going hunting for bighorn sheep, say, at least if you don’t live in an area that has them. Deer hunting and turkey hunting are practiced by individuals from a variety of backgrounds, but I strongly suspect they skew poor relative to the population as a whole. Raccoon, possum, and squirrel hunting are definitely “rural poor” activities, even if they’re sometimes practiced by wealthier folks who are still culturally working class and rural as well.