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To understand and answer why the British believed that the partition of India was necessary individuals need to know what influence the British had on India in the period of time the partition of India occurred, what the partition of India is and the impact that the partition of India has had and in return one is able to understand why the British believed that the partition of India was necessary. To gain this knowledge a wide range of resources need to be peruse for instance academic websites and journal articles by respected historians need to be used. Such resources include documents from UCLA that explore the partition of India in terms of the relationship that the two countries shared, The UK department for International Development's Yvan Guicheaua, who explores the processes of violent political mobilisation, which is an overview of contemporary debates and crise findings, Saumitra Jha and Stevens' article demonstrates the effects of the 'ethnic cleansing' while exploring reposition of populace. Another informative article is Mridu Rai article which explores the effects that the partition of India has had on the people of India and Pakistan, it also shows their perceptions of Pakistan and its founder, Mansergh's book explores the Indian army and colonial legacy demonstrates the world wars in which India supported Britain, it shows the effects that it had on the Indians. Finally another useful tool is Hist107 lecture slides which explored British Rule and the partition of India. When reading and understanding these resources and factors involved with the partition individuals are competent to understand why the British believed that the partition of India was necessary.
To begin with, it is important to understand the influence that the British had in India before the partition of India. The relationship between the British and India begin on the 31st of December 1600 when a group of merchants integrated themselves into the East India Company and were given supremacy on all dealings with the East Indies. The company's first cargo arrived in India via ships at the port of Surat in 1608.  In 1615 King James I gained the rights for the British to ascertain a factory at the port of Surat and in turn the British overshadowed the Portuguese and were able to witness a substantial expansion of their trading venture in India.  The below is a influential quote which demonstrates the influence the relationship that has began forming between the Indians and the British that have started settling onto the Indian continent.
"In the middle of the seventeenth century, Asia still had a far more important place in the world than Europe." So wrote J. Pirenne in his 'History of the Universe', published in Paris in 1950. He added, "The riches of Asia were incomparably greater than those of the European states. Her industrial techniques showed a subtlety and a tradition that the European handicrafts did not possess. And there was nothing in the more modern methods used by the traders of the Western countries that Asian trade had to envy. In matters of credit, transfer of funds, insurance, and cartels, neither India, Persia, nor China had anything to learn from Europe." 
This quote demonstrates the position which the East India Company brought upon them when they began its trading with Britain in the early 17th century. Manifestly the British had embarked on India in exploration to sell British exports to Continental Europe, but discovered little demand for the produce. Likewise to the Portuguese they discovered numerous Indian made products that they could traffic in Britain at a profit.  These factors are what established the monopoly that Britain had over India, this manipulation relationship started early on in the formation of British India.
Subsequently it is important to understand what the partition of India ensued. The Partition of India was the progression of separating the subcontinents. This process which took place in 1947 allowed India to achieve its independence from the British Raj. The Northern, primarily Muslim unit of India became the country of Pakistan, while the Southern and preponderance Hindu section developed into the Republic of India.  The partition of India was associated with mass violence and 'ethnic cleansing' where there were over 2 million deaths of Muslims, Hindus and Sikhs, in attendance were also over 75000 women and children who were raped in addition 12-15 million people where compulsorily relocated between the two countries.  The partition of India was related to India wanting its independence from Britain; during World War II the British sought India once again to provide essential soldiers and materiel for the war effort. The INC was hostile about sending Indians to battle and go down in another British war due to the unfaithfulness following World War I, the INC distinguished no benefit for India in the sacrifice of the war. The Muslim League conversely decided to support Britain's call for volunteers during an effort to gain British favour in support of a Muslim realm in post-independence northern India. As independence approached the country commenced to descend towards a sectarian civil war. 
In February of 1947, the British government proclaimed that India would be established independence by June 1948. With the country sliding further into pandemonium, Mountbatten unwillingly settled to the formation of two separate nations and with this moved the independence date up to August 15, 1947.  By course of the assessment in favour of partition completed, the parties subsequently faced the impractical task of completing a border between the new states.  Muslims engaged two main districts in the north of the subcontinent on opposite sides of the country which was separated by a majority-Hindu section in between the districts. In addition, all over most of northern India associates of the Muslim and Hindu religions were mixed with the population of people who were of Sikhs, Christians and other marginal faiths.  In the wealthy and fertile region of the Punjab, the problem was extreme with an equal combination of Hindus and Muslims. Neither side wanted to relinquish this valuable land, nor sectarian hatred ran high. The border was drawn right down the middle of the province, between Lahore and Amritsar.  On both sides, people scrambled to get onto the "right" side of the border, or were driven from their homes by their erstwhile neighbours. At least 10 million people fled north or south, depending upon their faith. On August 14, 1947, the Islamic Republic of Pakistan was founded. The following day, the Republic of India was established to the south. 
Finally now through understanding what the partition of India was, and why it happened individuals can now understand why the British believed that the partition of India was necessary. Through looking at the evidence presented clearly the reason for why the British believed that the partition of India was necessary was due to India gaining its independence. One of the main thoughts of why the British thought that the partition of India was necessary was because the Muslim people of India wanted their own separate state  . This factor plays a major role in the reasons behind why the partition of India occurred.
Once it is understood the influence that British had on India at the time of the partition, what the partition was and the reactions it had individuals are able to understand why the British believed that the partition of India was a necessary thing to do. Through reading a range of sources from Yvan Guicheaua, Saumitra Jha and Steven, Mridu Rai, Mansergh and using websites such as UCLA history and politics individuals are able to clearly see that even though the partition of India had negative effects such as the mass violence and 'ethnic cleansing' where there were over 2 million deaths of Muslims, Hindus and Sikhs, in attendance were also over 75000 women and children who were raped in addition 12-15 million people where compulsorily relocated between the two countries  . The Partition of India was actually something that the Muslim Indians wanted due to wanting their own separate state and the British were trying to assist them when India gained its independence from British India.