Just to cover some additional aspects of this discussion...
Many Canals were owned by Railways. For example the Kennet and Avon was owned by the GWR and the Birmingham Canal Navigations were at least leased by the London & Birmingham Railway from 1848.
The reasons for this were various. Sometimes the canal was a competitor, like the K&A, sometimes the canal came with the purchase of land or was brought to stop the canal shareholders objecting to the act for the new railway. In other cases the canal was purchased to give access to the area served by a rival railway.
There were a number of waterway and railway interchanges around both systems. Perhaps the biggest was at Brentford Dock in West London where the GWR had a large interchange between its lines and the Barges that worked the Thames, including those bringing goods up from seagoing ships in the docks further downriver, and the Narrowboats that worked the Grand Union.
Both the GWR and LMS operated a fleet of their own boats, 'Station Boats' to those of us on the cut, that operated from their interchanges ('Station Arms').
At least one canal owned its own railway. The Manchester Ship Canal Railway worked the docks area in Manchester and connected to local businesses and the larger railway companies in the area with the docks. It wasn't nationalised and survived in operation until 2009.
When the Railways were nationalised in 1948 the docks and canals that they owned came with them - somewhat to the surprise of the Department for Transport! You can gauge how much of the canal network was railway owned by that time by the fact that the government body that runs the canals, British Waterways, owns the vast majority of the canal system - everything they own came to the government as a 'free gift' with the railways.