The Limehouse Cut is a short canal in East London open since 1769 that connects the Lee Navigation to the Regent's Canal at Limehouse Basin. The canal begins (or ends depending on your point of view) at Bow Locks.
It then travels 2 miles through Tower Hamlets until it meets the Regent's Canal at Limehouse Basin which is where the canal joins the Thames. Originally the Limehouse Cut connected directly onto the Thames but that was changed in 1968 because of the need to replace the river lock. Instead a new short length of canal was built to connect the Limehouse Cut to Limehouse Basin allowing traffic to use the river lock there instead.
Nowadays the canal is used for leisure of course. Part of the Limehouse Cut was used during the final Olympic baton relay in 2012 due to the proximity of the canal to the Olympic stadium. I've visited the canal twice and walked its whole length. You can see my photos here and here.