In England, I think it can be a matter of buying the land either side of the river, but whether its owner controls navigation seems to be contested.
The UK Environment Agency says watercourses (including rivers) in England can be privately owned. [0]
British Canoeing seems to say that access to most navigable waterways in England is contested, including as trespass: "Of the 42,700 miles of inland waterways in England, only 1,400 miles can be paddled uncontested - that is a mere 4% of what is available. Paddlers are subject to challenge or dispute over their right to be on the water. ...If you are paddling on a river, lake or other waters where there is a disputed public right of navigation, then it could be alleged you may be trespassing." [1]
I think watercourses are a proper subset of waterways, with lakes being an example of waterways that aren't watercourses.
The right of owners to control fishing in England (and Wales) seems not to be contested in the way navigation is: "While the national rod licence gives a licence to fish anywhere in England and Wales, you might still need permission from the riparian owner to fish from her/his stretch of the river bank. The owner of the land adjoining one side of a natural river or stream owns the exclusive fishing rights (called, riparian rights) on her or his side of the bank. These rights extend up to the middle of the water. They can be leased or sold as separate property right (apart from ownership of the land itself). So, the owner does not necessarily have the right to fish from her/his side of the bank. An owner whose land adjoins a pond or lake has similar rights which extend as far as the middle of the water unless it encircles the pond or lake." [2]
Well, we have bugger all navigable waterways, even if a Kiwi did invent the modern jet-boat to increase the potential to navigate our braided rivers (in a rather small boat). [0]
In terms of rights to access rivers, it's complicated. There's the myth of the Queen's Chain [1], which has a kernel of truth in it, in very specific circumstances, but people had assumed it was far more broad reaching than it is.
And then there's the Ad Medium Filum Aquae (AMF) concept from English common law:
> By the common law, ownership of land adjoining a watercourse, which is not owned by the Crown, gives rise to the presumption that title extends to the middle line. It is a rebuttable presumption - that is, evidence to rebut (disprove) the presumption is always admissible.
That said, a lot of the riverbeds and banks of the larger (by our standards) rivers are owned by regional councils - we run three levels of government, central, regional, and local, and regional is the most focused on water allocations and flood management, so giving them ownership of the riverbeds and floodbanks around flood-prone rivers is a no-brainer - so AMF doesn't come up too often, but if you hunt for rabbits or similar, which love the braided riverbeds, then knowing where AMF applies and doesn't is vital to not meeting a grumpy farmer.
Unlike (what I've been told about) the UK, no-one can actually own the fishing rights to a river, nor the fish in the river. But you can own the land neighbouring it.
And yeah, that's how you privatise a river - buy land on both sides of the river from farmers who had previously reached an agreement with the Department of Conservation or similar to allow angler access via specified routes, and then rescind that access.
Of course, you can claim that you're not privatising the river because _technically_ the prime trout fishing stretch that your land now surrounds can be accessed via a hike upstream from Crown land that only takes 3 days one way.
I mean technically, yes, it's not privatised, but realistically, it pretty much is.
That said, the Crown is getting smarter about this, and is focusing more on permanent easements instead of relying on the goodwill of land owners - especially when rich American celebrities start buying up large high country farms, they tend to be rather... ...private, and thus averse to the public continuing to cross their land.
