Is the topology of weak convergence of probability measures first-countable?

Question

Let $S$ be a separable metric space, and $\mu,\mu_1,\mu_2,\ldots$ be Borel probability measures on $S$. We know that $\mu_n \to \mu$ weakly if and only if $\pi(\mu_n,\mu) \to 0$ where $\pi$ is the Prokhorov metric. However, this (a priori) doesn't imply that the metric topology induced by $\pi$ is the same as the topology of weak convergence of probability measures (which is the smallest topology such that $\mu \mapsto \int f \,d\mu$ is continuous for all continuous bounded $f:S \to \mathbb{R}$), since the topology of weak convergence of probability measures might not be first-countable. So my question is: is the topology of weak convergence of probability measures on $S$ first-countable? Thank you in advance.