The range of recently discovered phenomena in complex oxide heterostructures, made possible owing to advances in fabrication techniques, promise new functionalities and device concepts(1-3). One issue that has received attention is the bistable electrical modulation of conductivity in ferroelectric tunnel junctions(4-6) (FTJs) in response to a ferroelectric polarization of the tunnelling barrier, a phenomenon known as the tunnelling electroresistance (TER) effect(7-10). Ferroelectric tunnel junctions with ferromagnetic electrodes allow ferroelectric control of the tunnelling spin polarization through the magnetoelectric coupling at the ferromagnet/ferroelectric interface(11-17). Here we demonstrate a significant enhancement of TER due to a ferroelectrically induced phase transition at a magnetic complex oxide interface. Ferroelectric tunnel junctions consisting of BaTiO3 tunnelling barriers and La0.7Sr0.3MnO3 electrodes exhibit a TER enhanced by up to similar to 10,000% by a nanometre-thick La0.5Ca0.5MnO3 interlayer inserted at one of the interfaces. The observed phenomenon originates from the metal-to-insulator phase transition in La0.5Ca0.5MnO3, driven by the modulation of carrier density through ferroelectric polarization switching. Electrical, ferroelectric and magnetoresistive measurements combined with first-principles calculations provide evidence for a magnetoelectric origin of the enhanced TER, and indicate the presence of defect-mediated conduction in the FTJs. The effect is robust and may serve as a viable route for electronic and spintronic applications.