We calculated QED corrections to the $E1$ transition amplitudes in neonlike iron and nickel. For the $2p\phantom{\rule{0.16em}{0ex}}\ensuremath{\rightarrow}\phantom{\rule{0.16em}{0ex}}3d$ transitions the dominant effect came from the many-electron mixing or electronic correlations. For the $2p\phantom{\rule{0.16em}{0ex}}\ensuremath{\rightarrow}\phantom{\rule{0.16em}{0ex}}3s$ transitions the correlation and one-electron effects were comparable and tended to compensate each other. Our ab initio calculations showed that vertex corrections were negligible for both types of transitions. Other QED corrections were accurately reproduced by including effective QEDMOD operator in the many-electron relativistic configuration interaction calculation.