Yes, Auld Lang Syne.

A small number of the compositions of Rabindranath Tagore (Nobel prize laureate) were deeply influenced by English, Irish and Scottish folk music. Other songs he's used are The Vicar of Bray, The British Grenadiers, Go Where Glory Awaits Thee, and Robin Adair. He had a great many other influences, of course, among them various forms of music in India -- classical, baul and other folk forms.

I think he was quite travelled, as was his family, so he got these either directly from the West or through members of his family. I don't think it was the result of the British Raj in India.