Among recently discovered ferroelectricity-related phenomena, the tunnelling electroresistance (TER) effect in ferroelectric tunnel junctions (FTJs) has been attracting rapidly increasing attention owing to the emerging possibilities of non-volatile memory, logic and neuromorphic computing applications of these quantum nanostructures. Despite recent advances in experimental and theoretical studies of FTJs, many questions concerning their electrical behaviour still remain open. In particular, the role of ferroelectric/electrode interfaces and the separation of the ferroelectric-driven TER effect from electrochemical ('redox'-based) resistance-switching effects have to be clarified. Here we report the results of a comprehensive study of epitaxial junctions comprising BaTiO(3) barrier, La(0.7)Sr(0.3)MnO(3) bottom electrode and Au or Cu top electrodes. Our results demonstrate a giant electrode effect on the TER of these asymmetric FTJs. The revealed phenomena are attributed to the microscopic interfacial effect of ferroelectric origin, which is supported by the observation of redox-based resistance switching at much higher voltages.