The numerical study of QED radiative corrections in the low $x$ region for the H1 experiment at HERA was performed. The analytical program TERAD91 was used to get the size of the radiative corrections for the measurement of the proton structure function $F_2(x,Q^2)$ in the range $x= 10^{-2} - 10^{-4}$ and $ 5 GeV^2 < Q^2 < 80 GeV^2$. It was found that radiative corrections can be not small in some points of the phase space of the mixed variables.