We investigate the torque field and skyrmion movement at an interface between a ferromagnet hosting a skyrmion and a material with strong spin-orbit interaction. We analyze both semiconductor materials and topological insulators using a Hamiltonian model that includes a linear term. The spin torque inducing current is considered to flow in the single band limit therefore a quantum model of current is used. Skyrmion movement due spin transfer torque proves to be more difficult in presence of spin orbit interaction in the case where only interface in-plane currents are present. However, edge effects in narrow nanowires can be used to drive the skyrmion movement and to exert a limited control on its movement direction. We also show the differences and similarities between torque fields due to electric current in the many and in the single band limits.