Calculating the quasiparticle (QP) band structure of two-dimensional (2D) materials within the GW self-energy approximation has proven to be a rather demanding computational task. The main reason is the strong q-dependence of the 2D dielectric function around q = 0 that calls for a much denser sampling of the Brillouin zone than is necessary for similar 3D solids. Here we use an analytical expression for the small q-limit of the 2D response function to perform the BZ integral over the critical region around q = 0. This drastically reduces the requirements on the q-point mesh and implies a significant computational speed-up. For example, in the case of monolayer MoS2, convergence of the G0W0 band gap to within ∼ 0.1 eV is achieved with 12× 12 q-points rather than the 36×36 mesh required with discrete BZ sampling techniques. We perform a critical assessment of the band gap of the three prototypical 2D semiconductors MoS2, hBN, and phosphorene including the effect of self-consistency at the GW0 and GW level. The method is implemented in the open source GPAW code.