In English law, wild deer belong to the Crown—a principle dating to Norman forest law. But "ownership" doesn't mean what you might think.
All wild deer (red, fallow, roe, sika, muntjac, Chinese water deer) are legally res nullius (nobody's property) until captured or killed, at which point they become the property of the landowner—or the Crown, if taken illegally. The Crown's "ownership" is really a regulatory sovereignty: the power to grant or restrict hunting rights.
Medieval kings created royal forests (not necessarily wooded) where only they and grantees could hunt. Commoners retained rights in some areas (forest law vs. common law). Over centuries, these evolved into:
Today, landowners control deer on their land—culling for crop protection, managing populations, selling stalking rights. The Crown exercises its theoretical title mainly through licensing (e.g., night shooting, selling venison) and conservation designations (SSSIs). Private deer parks operate as commercial ventures.
So: Crown owns the right to regulate; landowner owns the right to manage and harvest; poacher gets prosecuted.