Tales Of The 77th Bengal Lancers was a television series that lasted for a year and starred Philip Carey and Warren Stevens as a pair of young lieutenants assigned to said regiment and their exploits holding the crown jewel of the British Empire for their Queen. Their commanding officer was Patrick Whyte who actually was in the Indian army during the final days of the British Raj.
Other than that the series never got closer to India than the Indian elephants and tigers at the San Diego Zoo. It was shot here in the USA for that year it ran. A decade later the television series Maya which actually was shot in India was canceled frankly because of the expense of location shooting.
Not to say that some decent films weren't done about the Raj in America. One could mention Lives Of A Bengal Lancer, The Charge Of The Light Brigade, Gunga Din all of which have their fans. All of them good as they are never quite got the British experience in India, let alone the Indian experience of having them there quite right.
Those were all A pictures and Tales Of The 77th Bengal Lancers was a television series and would have qualified as B films back in the day. The native Indians were treated a lot like our American Indians and Carey and Stevens could have been in our frontier cavalry. I noticed the name of George Archaimbaud as a director of episodes of the show and Archaimbaud was a well known director of B westerns, a lot of the Hopalong Cassidys for instance. That should tell you all you need to know.
I haven't seen any episodes in decades, at least since the Sixties when it passed out of syndication. I remember as a kid just enjoying it as a western where the cavalry wore helmets and the Indians wore turbans. At least the officers wore helmets.