Using a suite of detailed numerical simulations we estimate the level of anisotropy generated by the time evolution along the light cone of the 21cm signal from the epoch of reionization. Our simulations include the physics necessary to model the signal during both the late emission regime and the early absorption regime, namely X-ray and Lyman-band 3D radiative transfer in addition to the usual dynamics and ionizing UV transfer. The signal is analysed using correlation functions perpendicular and parallel to the line of sight (LOS). We reproduce general findings from previous theoretical studies: the overall amplitude of the correlations and the fact that the light cone anisotropy is visible only on large scales (100 cMpc). However, the detailed behaviour is different. At 3 different epochs, the amplitude of the correlations along and perpendicular to the LOS differ from each other, indicating anisotropy. These 3 epochs are associated with 3 events of the global reionization history: the overlap of ionized bubbles, the onset of mild heating by X-rays in regions around the sources, and the onset of efficient Lyman-alpha coupling in regions around the sources. A 20x20 deg^2 survey area may be necessary to mitigate sample variance when we use the directional correlation functions. On a 100 cMpc scale the light cone anisotropy dominates over the anisotropy generated by peculiar velocity gradients computed in the linear regime. By modelling instrumental noise and limited resolution, we find that the anisotropy should be easily detectable by the SKA, assuming perfect foreground removal, the limiting factor being a large enough survey size. In the case of the LOFAR, it is likely that only first anisotropy episode will fall in the observing frequency range and will be detectable only if sample variance is much reduced (i.e. a larger than 20x20 deg^2 survey, which is not presently planned).
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