It all hangs on the fact that in most cases, the person who owns the land, owns the river bed to half way across the river and the accompanying fishing rights. He doesn't own the water and the fish are feral, no one owns them (except in lakes where its a bit different). So then the person who owns the land leases (or licences) off the fishing rights to a club or other individual/body and they can then control who fishes there.
In cases where the Environment Agency own the land and the river bed and the fishing from the bank is deemed to be free fishing, then fishing from a boat also would be allowable. You're right about tidal stretches, but
ask around as some funny rights and laws exist from the writing of the Magna Carta*. It's worth checking about the bits of river you intend to fish, a lot of land owners don't mind, many don't care, but I know one person who is very funny about it and it now transpires that he may not have the rights anyway.
It's very confusing...
* Mark beat me to it, I think it's something about the first bridge in some cases as well.