This proposal is part of our research programme to explore novel ground states in frustrated quantum magnets. Strong spin-orbit coupling is predicted to stabilize composite spin-orbital moments for Ir4+ and this combined with a honeycomb lattice could lead to strongly-frustrated interactions that could stabilize quantum spin liquid or unconventional magnetic orders. In recent inelastic measurements on Li2IrO3 using MERLIN we observed strongly dispersive magnetic excitations with a softening wavevector corresponding to a large magnetic unit cell not accounted for by current theoretical models. In preliminary WISH measurements we observed one magnetic Bragg peak (at the softening wavevector of the inelastic scattering), and here we propose a higher-accuracy measurements to attempt to observe some higher order Bragg peaks as those are essential to solve the magnetic structure.