Yep, but that E field is generated from currents in the lossy seawater, and those currents are induced by the magnetic field. If the seawater were a perfect conductor, the magnetic field would not propagate either.

Free space impedance is 377 Ohms/meter; the ratio of E/H fields. Seawater is much, much lower, but the ratio is still there. If there's a propagating H field, there is a corresponding E field; that's the law according to Maxwell.

The VLF antennas on the subs are trailing wires; electrically short dipoles. Those are mostly sensitive to E fields.