  We study the effect of Coulomb repulsion between oxygen holes on the London
penetration depth $\lambda$ based on the concept of spin-polaron nature of
Fermi quasiparticles in cuprates superconductors. It is shown that for the
generally accepted values of the parameters of the spin-fermion model, taking
into account the Coulomb interaction, both the one-site Hubbard $U_p$ and
interaction between the holes on next-nearest-neighbor oxygen ions $V_2$,
allows one to achieve a much better agreement of the calculated temperature
dependencies of the value $\lambda^{-2}$ with the experimental data in
La$_{2-x}$Sr$_{x}$CuO$_4$ in a wide range around optimal doping.
