From Prandle 19791:

The flow of water across the vertical component of the Earth's magnetic field induces a potential gradient in the water; measurements of the difference in voltage between the opposite sides of a tidal channel provide an indication of the magnitude of the tidal flow

I imagine that having a cable across the channel enables an accurate comparison of voltage on either side.

I suspect that this is a large-scale example of the Hall Effect, but that part of my physics is too rusty to say for sure!

1 D. Prandle, "Anomalous results for tidal flow through the Pentland Firth", Nature vol 278, pp 541-542 http://www.homepages.ed.ac.uk/shs/Tidal%20Stream/Prandle%20phase%20anomaly.pdf

Maxwell showed that the motion of electrically charged particles in any magnetic field creates an electric field. The two fields would be perpendicular to one another. As seawater containing a large amount of ions (it is salty after all) moves through Earth's magnetic field in ocean currents, it generates the an electric field that as the theory predict will be perpendicular to the water current. The electric field is the result of the vertically average effect of the ocean motion. When a submarine cable is available between two points, the change in electrical current at both ends of the cable can be measured. The change will be proportional to the "vertically integrated ocean current" or ocean current transport (the total flux of water through a given area).

The first demonstrations were conducted by Henry Stommel in the 1950's. A full array of measurements are conducted in the Florida Straits taking advantage of submarine cables connecting Florida and Bahamas. The sources of errors and variability were discussed by Larsen, 1992.

NOAA AOML provides a good description of the theory and applications.

Stommel, H., 1957. Florida Straits Transports, 1952-1956. Bulletin of Marine Science, 7(3), pp.252-254.