Existence and uniqueness are proved for McKean-Vlasov type distribution dependent SDEs with singular drifts satisfying an integrability condition in space variable and the Lipschitz condition in distribution variable with respect to $\W_0$ or $\W_0+\W_\theta$ for some $\theta\ge 1$, where $\W_0$ is the total variation distance and $\W_\theta$ is the $L^\theta$-Wasserstein distance. This improves some existing results derived for drifts continuous in the distribution variable with respect to the Wasserstein distance.