I have just received an email from BCU regarding "Go canoeing week" and advertising guided trips on the Beaulieu River.
The relevant website is:
"As the River is privately owned and managed by Beaulieu Estate, you’ll still need to come along at the allocated time slots."
"The River is tidal so timings have been devised to make the most of each day."
I do not know the local details but can a tidal river be privately owned?