The extreme field confinement and electro-optic tunability of plasmons in graphene make it an ideal platform for compact waveguide modulators, with device footprints aggressively scaling orders of magnitude below the diffraction limit. The miniaturization of modulators based on graphene plasmon resonances is however inherently constrained by the plasmon wavelength, while their performance is bounded by material loss in graphene. In this report, we propose to overcome these limitations using a graphene-covered lambda/1000 plasmonic nanogap waveguide that concentrates light on length scales more than an order of magnitude smaller than the graphene plasmon wavelength. The modulation mechanism relies on interference between the non-resonant background transmission and the transmission mediated by the gate-tunable nanogap mode, enabling modulation depths over 20 dB. Since the operation of the device does not rely on graphene plasmons, the switching behavior is robust against low graphene carrier mobility even under 1000 cm(2)/Vs, which is desirable for practical applications. (C) 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement