I remember people eel trapping when I was a kid. The traps were wire mesh but traditionally they were made of willow and were designed like a narrow lobster pot. If you look at the first picture in this article from the Fish Museum, it shows a structure built in the water to tether the traps to I suppose to stop them drifting away. Can't think what the brickwork was for that you mention, unless perhaps poles were laid across the top of two brick walls to tether the pots.

http://www.fishingmuseum.org.uk/eel_bucks.html