The tunnelling current caused by electron transfer between two-dimensional layers is calculated as a function of the magnetic field applied perpendicular to the layers and level splitting of the tunnel-coupled states. The elastic scattering of the electrons is taken into consideration. Analytical results describing both the tunnelling relaxation rate of photoexcited electrons and the tunnelling current between the independently contacted quantum wells are obtained for two regimes: (i) that of small magnetic fields, for which the Landau quantization is suppressed by the scattering and the oscillating part of the current shows nearly harmonic behaviour; and (ii) that of high magnetic fields, for which the Landau levels are well defined and the current shows a series of sharp peaks corresponding to resonant magnetotunnelling. In the latter case, we used two alternative approaches: the self-consistent Born approximation method and the path-integral method, and demonstrated that the results obtained show reasonable agreement for both of these methods. The influence of the interlayer correlation of the scattering on the first magnetotunnelling peak is also discussed.