The $O(\alpha)$ electromagnetic radiative corrections to the $B^- \rightarrow V^0 \ell^- \bar{\nu}_{\ell}$ ($V$ is a vector meson and $\ell$ a charged lepton) decay rates are evaluated using the cutoff regularization and the soft-photon approximation. Model-dependent parts of real photon corrections involving intermediate resonance states are also considered. The cutoff dependence of radiative corrections upon the scale $\Lambda$ that separates the long- and short-distance regimes is found to be mild and is considered as an uncertainty of the calculation. These corrections will be relevant for a precise determination of the $b$ quark mixing angles by testing isospin symmetry when measurements of semileptonic rates of charged and neutral $B$ mesons at the few percent level become available.