Efficient switching of power (> 95%) between an optical fibre, side polished close to the core, and a high index multimode overlay waveguide can be induced by variation of the overlay waveguide parameters. Using lithium niobate sandwiched between two optically transparent indium-tin-oxide electrodes as the overlay, electro-optic switching has been observed. By applying a second side-polished fibre to the overlay top surface, power may be switched between the two fibres. The feasibility of such an electro-optically controlled optical fibre routing switch is demonstrated.