A few of the British companies running to India over that time span;
P and O.
The other route NY to India - could be via the UK or continent so the number of shipping companies that would have traded to India are enormous. I have put a link that shows an alphabetical list of shipping companies. Not all by any means traded on the India routes but to give you any idea of the difficulty of your search. Without some more information - shipping company - ships name etc etc you have a mammoth task.