The identification of sources driving cosmic reionization, a major phase transition from neutral Hydrogen to ionized plasma around 600-800 Myr after the Big Bang (Dayal et al. 2018, Mason et al. 2019, Robertson et al. 2022), has been a matter of intense debate (Robertson et al. 2022). Some models suggest that high ionizing emissivity and escape fractions ($f_{\rm esc}$) from quasars support their role in driving cosmic reionization (Madau & Haardt 2015, Mitra et al. 2018). Others propose that the high $f_{\rm esc}$ values from bright galaxies generates sufficient ionizing radiation to drive this process (Naidu et al. 2020). Finally, a few studies suggest that the number density of faint galaxies, when combined with a stellar-mass-dependent model of ionizing efficiency and $f_{\rm esc}$, can effectively dominate cosmic reionization (Finkelstein et al. 2019, Dayal et al. 2020). However, so far, low-mass galaxies have eluded comprehensive spectroscopic studies owing to their extreme faintness. Here we report an analysis of eight ultra-faint galaxies (in a very small field) during the epoch of reionization with absolute magnitudes between $M_{\rm UV}$ $∼ -17$ to $-15$ mag (down to 0.005 $L^{⋆}$. We find that faint galaxies during the Universe's first billion years produce ionizing photons with log($ξ_{\mathrm{ion}}$/ Hz erg$^{-1}$) =$25.80± 0.14$, a factor of 4 higher than commonly assumed values (Robertson et al. 2015). If this field is representative of the large scale distribution of faint galaxies, the rate of ionizing photons exceeds that needed for reionization, even for escape fractions of order five per cent.