Theorem 2.6.6 in “USCO and Quasicontinuous mappings”, vol. 81, Berlin, Boston: De Gruyter, 2021, by L.Hola, D.Holy and W.Moors says (more-or-less): 

If $f:H\times X \to G$ is a separately continuous mapping, $H$ is a Cech-complete topological group, $X$ is a $q$-space, $G$ is a topological group, and for each $x \in X$, $h \mapsto f(h, x)$ is a group homomorphism, then $f$ is jointly continuous on $H\times X$.

But perhaps this is too general for your purposes.