Electroactive actuators have received enormous interest for a variety of biomimetic technologies ranging from robotics and microsensors to artificial muscles. Major challenges towards practically viable actuators are the achievement of large electromechanical deformation, fast switching response, low operating voltage and durable operation. Here we report a new electroactive actuator composed of self-assembled sulphonated block copolymers and ionic liquids. The new actuator demonstrated improvements in actuation properties over other polymer actuators reported earlier, large generated strain (up to 4%) without any signs of back relaxation. In particular, the millimetre-scale displacements obtained for the actuators, with rapid response (<1 s) at sub-1-V conditions over 13,500 cycles in air, have not been previously reported in the literature. The key to success stems from the evolution of the unique hexagonal structure of the polymer layer with domain size gradients beneath the cathode during actuation, which promotes the bending motion of the actuators.