  We present the results of a search for a hidden mirror sector in positronium
decays with a sensitivity comparable with the bounds set by the prediction of
the primordial He$^{4}$ abundance from Big Bang Nucleosynthesis. No excess of
events compatible with decays into the dark sector is observed resulting in an
upper limit for the branching ratio of this process of $4.0\times10^{-5}$
($90\%$ C.L.). This is an order of magnitude more stringent than the current
existing laboratory bounds and it constraints the mixing strength of ordinary
photons to dark mirror photons at a level of $\varepsilon<5.8\times 10^{-8}$.
