Question

Describe the relationship between Britain and India from start to finish?

Answer 1

To make sure that the answer is relevent to us today , I'll only be looking at the period after 1947 when India had already become independent. 
Any answer based on the period before 1947 is not something I can reasonably hope to answer rationally. Mainly because of two important factors that I can't  quantify . 
1. How do you quantify human life and suffering ?
2. How do you quantify civilization, ideas of democracy and the modern liberal way of thinking ?

So to answer the question after the British left in 1947 , frankly for the British , India was a sinking ship. They had taken all that they could and after World War II had too much on their plate to consider India important enough to deal with . So the British mindset was more often than not the West's mindset. And for much of the later half of the 20th century , India was perceived by the West to be closer to USSR and hence a natural distrust developed. Both US and England spent this time watching India warily. 

There are singular points which have marked US/UK relations with India . 
1. 1962 war is declared between India and China. US and by proxy UK support India to counter the rise of the communists. 
2. 1971.Bangladesh war of independence. US parks its naval fleet(Task Force 74) near India to deter any Indian misadventures. Nixon/Kissinger develop a healthy mistrust for Indira Gandhi. UK follows the US lead and deploys a carrier battle group led by HMS Eagle to the Bay of Bengal.
3.1997.  UK Foreign Minister Cook  was quoted in Islamabad ,saying that UK could act as  a mediator between India and Pakistan on the Kashmir issue. Prime Minister Gujral who was in Egypt at that time was famously quoted as furiously calling England a third rate power who created the problem in the first place. Both refused to acknowledge their words when Cook meets Gujral along with the Queen of England. 
4.2009. UK Forign Secretary visited India in the aftermath of the Mumbai 2008 attacks . He infamously said that India should resolve the Kashmir issue with Pakistan so that Pakistan could focus on its West Border with Afghanistan. He also said that if India had solved the Kashmir issue , the Mumbai attacks would not have happened. This made one of the senior Indian bureaucrat's call him out saying that we(India) do not advise Britain on Ulster(Ireland) and neither should Britain lecture us . The Miliband trip was hailed as an unmitigated disaster on both sides and further worsened the relationship.

With reference to these instances and more , I would like to point out that even after Independence , India's relation with UK has been fraught with dialogues from both side that have damaged the UK-India relationship . Also Indian bureaucrat's and elite have formed the notion that UK cannot be trusted when push comes to shove and have largely made no effort to promote the relationship. Also the UK Labour party has at multiple times pandered to the efforts of the Pakistani nationals and expats living in UK.  

So in conclusion the Indian-UK relations are much more worse than both Governments care to admit . On the Indian side their is distrust of UK at the highest levels while the English side has historically been ignorant of the intricacies of India-Pakistan relations and hence have made that ignorance public multiple times . 

It should be noted , however that Prime Minister Cameroon and Prime Minister Modi are trying to turn this relationship but it remains to be seen whether they actually succeed. hope that helped