(Editing this post much later I have probably got it wrong on the old maps. The canals they show are more likely to refer to the other canal linking the Chao Phraya to the Bang Pakong, Klong Saen Saeb, which was built 40 years earlier. I am not sure on the waterway shown south of the Petrio Canal on the British map as this looks too far south for Klong Prawet Burirom.)
No walk today as never left this computer, just too busy. It's a bit late but I wanted to upload the two maps below. Both show the waterway connecting the two rivers, Chao Phraya and the Bang Pakong. The Klong Prawet Burirom was built between 1877 and 1880. The maps are dated 1886 and 1896.
Below is the 1896 map by Maxwell Sommerville, a visiting Professor of Glyptology from the University of Pennsylvania. (I'm still not sure what glyptology is.) It looks like he has based his map on an earlier work as the western end of the waterway is showing an existing river course rather than the canal. His trip was actually up the Chao Phraya rather than to the east of Bangkok so he wouldn't have seen it.
The second map is British from 10 years earlier and shows the klong, on this called the Petrio Canal. I will have to identify the towns shown with their modern names sometime. Maybe tomorrow I will get the Google Maps of my walking area up.