Quantum dots have been identified as potential sources of entangled photon pairs, essential for many applications in quantum information. However, in practice structural properties of the dots result in polarisation splitting of the emission lines, which has prevented the realisation of such a source. Here, we present two techniques developed to control the polarisation splitting in a quantum dot both irreversibly and reversibly. We find that the splitting is strongly dependent upon the emission energy, or lateral confinement, of the quantum dot. Thus by precise control of the InAs deposition thickness, it is possible to produce ensembles from which dots with zero polarisation splitting can be easily selected. Additionally, we demonstrate that by using modest in-plane magnetic fields to partially mix the bright and dark exciton states, the polarisation splitting can be reversibly tuned to zero for most dots of a certain type. Finally, we demonstrate the emission of triggered entangled photon pairs from a quantum dot with approximately zero splitting with fidelity > 70%.