Few-fs electron bunches from laser wakefield acceleration (LWFA) can efficiently drive plasma wakefields (PWFs), as shown by their propagation through underdense plasma in two experiments. A strong and density-insensitive deceleration of the bunches has been observed in 2 mm of 10^{18} cm^{-3} density plasma with 5.1 GV/m average gradient, which is attributed to a self-driven PWF. This observation implies that the physics of PWFs, usually relying on large-scale rf accelerators as drivers, can be studied by tabletop LWFA electron sources.