Were Sean Connery or Michael Caine in it? If both, then it's
The Man who would be King, but I'm not seing anything in the plot that sounds like what you're describing.
Edit: Oh, maybe it's
North West Frontier? Seems to have a few more of the elements you're looking for. Came out in 1959:
Synopsis for North West Frontier wrote:
In northwestern India soon after the turn of the 20th Century, Moslem rebels seek to kill a six-year-old Hindu prince to end his family line. Captain Scott of the British Army is ordered to get the prince out of the region safely. Adventure ensues as Scott sneaks the child away, through Moslem-held territory, by train. Also on board are the boy's American governess, an arms merchant, a cynical reporter, and two upper class Britons.