I think you are right about that.
The one that ran through Brockley and down to Croydon became the railway which currently follows the same course.
If you come out of Forest Hill station and cross the south circ the pavement has cobbles, as that is where the tow path once was.
OK so maybe that was some other canal I was being told about... perhaps the one that ran though Brockley was some other spur?