More specifically in what ways did the political, social and economic relationship change between the two? Also in what ways did British attitudes towards Indian culture change?
Not to be snide, but this sounds like a question lifted from a homework assignment.
Interesting you picked 1845 as your start point. So the British East India Company (EIC) a private company chartered by England, effectively ruled the Sub-continent using large privately funded armies until 1858. In 1858 the British assumed direct control with the creation of the British Raj. In 1877 Queen Victoria was proclaimed Empress of India to further tighten bonds and make it clear that all Indians were her subjects. The Raj was dissolved in 1947 with the creation of India and Pakistan. My guess is you all ready know this and want some one to explain the ever evolving social, political and economic environments on the Sub-continent and in Great Britten over this 102 year time frame. Suggest you take a look at "Raj: the Making and Unmaking of British India" by Lawrence James.