The short answer to you question why an Indian would believe that there was a secret deal between Gandhi and Britain is that they were probably a Hindu Nationalist, and a fairly fervent one at that.

It is important to remember that the Indian independence movement was a very broad tent movement that involved pulling together people of several different religions, many different ethnicities and languages, as well different classes and castes. There were many strands of thought in the movement that often disagreed with each other.

One major strand of the movement were Hindu nationalists. They called for the establishment of a Hindu state, ruled by Hindus along Hindu religious ideas. They saw Indian identity as not civic based but instead based along religious lines. They opposed Gandhi's inclusive vision of India and in particular and most importantly rejected his calls for non violence.

Men like Subhas Chandra Bose are examples. Bose at one point was President of the Indian National Congress but left because he felt violence was needed on top of Gandhi's tactics.

It should be remembered Gandhi was murdered not by the British but by a Hindu Nationalist who felt Gandhi had sold out India to Pakistan and rejected his non-violence.

As to your title question, the British decision to let India go is a long and complicated one. India independence occurred after some 30 years of negotiations as the British attempted to accommodate Indian demands while keeping it under British control. The decision in 1948 was taken ultimately because Britain lacked the political, economic and military power to rule India without some kind of consent by the Indians.

Source: A university level history course on the History of India, and Stanley Wolpert's a New History of India, which is very well done.