Did any Indian people become involved in politics or business in Britain? Were there cases of Indian people marrying Brits from well-to-do families?
Would a wealthy Indian be seen as better than a poor English or Irish person?
It could be done. Here is the case of one. (I don't think he was Hindu. He was a Sikh).
Frederick Duleep Singh, the younger son of Duleep Singh, the last Maharaja of the Sikh Empire, was born in London and educated at Eton and Magdalene College, Cambridge. (BA in history 1890, MA in history 1894).
He was a member of the University Pitt Club, and a Fellow of the Society of Antiquaries. He was a staunch monarchist, known for hanging a portrait of Oliver Cromwell upside down in the lavatory of his mansion at Blo' Norton.
He was a Lieutenant and Captain in the Suffolk Imperial Yeomanry from 1893-1901, when he transferred to the Norfolk Yeomanry and was promoted to Major. He resigned this commission in 1909 but rejoined during WWI and was on active service with the Norfolk Yeomanry in France for two years.
He was popular in aristocratic British circles, and known to his friends as "Prince Freddy".