Yes definitely. I live in a multicultural city in the midlands where white people are almost the minority.
I have experienced racism directly from the Indian/Pakistani/black communities on rare occasions.
I have particularly seen racism between the Pakistani and Indian communities, especially when westernised sons and daughters want to marry each other. Same for if they want to date or marry a white person. Some of the community teach their sons that white girls are to sleep around with and use to get experience before marriage.
My friend is a devout Christian and she is married to a Sikh. There was not an issue from either side of the families they just accepted each other and had 2 weddings and celebrate all the festivals etc.