While I certainly do not wish to paint the British with one brush, I do believe that the vast majority did view India and its people as in need of "civilization." The British came to India and determined that their role was to "enlighten" the dark country (literally and figuratively.) As Forster says, they came to be "little Gods" in India. Their desire to replace as many indigenous customs and practices with British ones would testify to this. Many British came to India and were unaware or unwilling to understand the customs and traditions which existed long before Britain had been in existence. They could not understand much of the religious devotion in a form of worship that had been around for thousands upon thousands of years. Instead, the British sought to remake India as Britain with more heat and sun. For a great deal of time, it worked, until the Independence movement struck a chord with many Indians.
As I understand it, Indian culture was treated by most British people as something of a curiosity. It was seen as quaint and backward. It was interesting, and there were things to be gained from it, but it was not to be taken seriously. So interest in Indian culture was sort of like the kind of interest tourists have -- they wanted to look at exotic things, but didn't think it was as good as British culture.
I think that this attitude and the way the British treated India sort of fed off of one another. I do not know that you can say that the one caused the other -- they sort of went hand in hand. Because the British did not respect the Indians, they did not respect their culture. Because they did not respect their culture, they did not respect the Indians and so on.
The view of of British people about the Indian culture was highly prejudiced and derogatory. This was partly because of natural arrogance of people who gain simply by belonging to victor group rather than by their own capabilities. Partly it was a part of planned strategy of the British to break down the moral strength and self respect of the Indians, to perpetuate the British rule. And they succeeded in their strategy very well. Thus many of the negative features of Indian society such as excessive oppression of lower class people, lack of innovation, obsequiousness, poverty and unemployment, famines and fatalism are more characteristic of India under the British rule rather than of earlier periods. It is worth while noting that the oppression of the rural people in India was aggravated a great deal by the Zamindari system introduced by the British in many parts of the country.
In general British people looked down upon everything Indian. However there were many independent British individuals who took interest in and studied Indian culture,read its old literature and investigated its past, and appreciated thing Indian. However such people constituted an insignificant minority.