I know the U.S.A was guilty of using white actors in dark makeup to play other ethnic groups, but you'd think that you could find a few east Indians in Britain to be in this film. I know, I'm being too sensitive. It was common for the times to do it this way, etc. But it really stands out.
You wouldn't encounter anything different in any other British production of that era - The Great St Trinians Train Robbery has a particularly awful example. Spike Milligan played an Indian in TV series of that era, and even the TV series It Ain't Half Hot Mum, which did at least have Indian actors playing Indians, had an Englishman playing the main Indian character (extremely accurately, according to an Indian friend of mine). It didn't start changing until around 1970-ish.
Indian characters rarely were played by Indians in the 60s or before. It was just the way things were, migration from the Indian subcontinent had barely begun at that time so the pool of Indian actors would have been small anyway. Plus, it wasn't that big a deal, we had other things to occupy our minds in the 60s and weren't obsessed with political correctness and race. We were actually allowed to laugh at each other then although now of course such monstrous criminals would be forced to beg the Almighty Twitter for forgiveness followed by a mandatory course of Correct Thinking and Acceptable Targets for Humor.
There are a lot more extreme examples. Mickey Rooney in "Breakfast at Tiffany's" (Japanese, not Indian, but same concept) must be in the vicinity of the high water mark.