In this paper we report the measurement of laser-driven proton acceleration obtained by irradiating nanotube array targets with ultrashort laser pulses at an intensity in excess of 1020 W cm-2. The energetic spectra of forward accelerated protons show a larger flux and a higher proton cutoff energy if compared to flat foils of comparable thickness. Particle-In-Cell 2D simulations reveal that packed nanotube targets favour a better laser-plasma coupling and produce an efficient generation of fast electrons moving through the target. Due to their sub-wavelength size, the propagation of e.m. field into the tubes is made possible by the excitation of Surface Plasmon Polaritons, travelling down to the end of the target and assuring a continuous electron acceleration. The higher amount and energy of these electrons result in turn in a stronger electric sheath field on the rear surface of the target and in a more efficient acceleration of the protons via the target normal sheath acceleration mechanism.