I couldn't find any reference to the .303 in "Maneaters of Kumaon", but maybe in one of the other books? Corbett appears to have used a ".500 modified cordite rifle", a DR .450/.400 and a .275.

J.H. Patterson used a .303 extensively in "The Man-Eaters of Tsavo and Other East African Adventures". He comments on its lack of knock-down power on lions, but I'm not sure that you would reasonable expect it to (!), especially with what were probably unsuitable bullets. Nevertheless he is usually at pains to defend the cartridge and at the end of the book suggests that "the battery, to be sufficient for all needs, should consist of a .450 express, a .303 sporting rifle, and a 12-bore shot gun".