  The 21~cm transition from neutral Hydrogen promises to be the best
observational probe of the Epoch of Reionisation. The main difficulty in
measuring the 21 cm signal is the presence of bright foregrounds that require
very accurate interferometric calibration. Closure quantities may circumvent
the calibration requirements but may be, however, affected by direction
dependent effects, particularly antenna primary beam responses. This work
investigates the impact of antenna primary beams affected by mutual coupling on
the closure phase and its power spectrum. Our simulations show that primary
beams affected by mutual coupling lead to a leakage of foreground power into
the EoR window, which can be up to $\sim4$ orders magnitude higher than the
case where no mutual coupling is considered. This leakage is, however,
essentially confined at $k < 0.3$~$h$~Mpc$^{-1}$ for triads that include 29~m
baselines. The leakage magnitude is more pronounced when bright foregrounds
appear in the antenna sidelobes, as expected. Finally, we find that triads that
include mutual coupling beams different from each other have power spectra
similar to triads that include the same type of mutual coupling beam,
indicating that beam-to-beam variation within triads (or visibility pairs) is
not the major source of foreground leakage in the EoR window.
