The British Empire in India, in one form or the other, spanned for almost 200 years. A lot of things change over such a long time span but a couple of things remained the same - the British were always considered "foreigners" (by both the British and the Indians) and the Indians who fought for them mostly did so for the money. They were also mostly volunteers and very loyal to their paymasters (as long as their sentiments were respected). Throughout their rule in India, the English were always the most reliable paymasters.

Early Empire

Back in the early 1700's when the European Companies were first building up sepoy armies (sepoy is term for an Indian soldier in a European army in India - its based on a mis-pronunciation of the Hindustani word Sipahi), there was no concept of pan-Indian nationalism. Under the rapidly declining Mughals, the loyalty of the average Indian depended very much on where they lived. The Mughal governors had relatively little local support, except when they could pay or had a significant local contingent of foreign fighters (usually Afghan, Central Asian and in some cases even 'Arab'). Local Rajahs (hereditary rulers who were in charge for generations) often could command more loyalty based on how their social conditions were organized, but these were invariably very small states. During this century we see time and time again, the English winning wars because of their ability to pay. The (ex-Mughal) Nizam of Hyderabad had a formidable French-trained army, which revolted when he could not pay them. The French officers defected (essentially escaped) to the English, who happily paid and disbanded the sepoy contingents. The Nizam then entered into a "subsidiary alliance" with the Company, under which the Company collected revenue from demarcated districts, and used it to pay for an English-trained army with English officers to protect the Nizam. The Nizam was happy because he could now stop paying taxes to his arch-rivals - the Marathas. Thus the Company won over what would remain the biggest princely state in India without firing a musket.

What helped the English was the complete absence of a sense of nationalism in India. Percival Spear addresses this in his Penguin's History of India - Volume 2:

... a further factor which was an essential element of the then Indian scene... the absence of the phenomenon of nationalism, then as since so dominant in Europe as to be taken for granted in assessing the political field. In India the horizontal divisions of caste and the vertical divisions of religion were more important than those of race...

The Indian soldiers were not mere mercenaries

The English Company in particular was very sensitive to religious sentiments, which helped keep the soldiers loyalty. Two of the most significant revolts, both involved religion: the Vellore mutiny in 1806 and the Great Indian Rebellion in 1857 (at least for the sepoys, fear of losing their religion/caste was a major factor). In both cases religion/caste was not the only factor, but it was the tipping point at which the soldier chose death over their orders.

After 1857 Christian missionary activity was again severely restricted (it was only allowed in 1833 at the insistence of Parliament, over the Company's better judgement).

The Rise of Nationalism

Post-1857, a new Indian English-educated middle class started to come up. They began to judge the English by their own standards and principles like liberty, freedom and self-rule, asking how the English could claim to stand by those and yet deny it to Indians. This group would come to represent a new Indian nationalism, which by WW-2 (which you mention) had essentially guaranteed that India would get self-rule. The war delayed this, but the British had to make a, "you will get anything you want after the war is over" offer, fund a huge military build-up and arrest a 100,000 political dissidents to hold India over the next few years. After the war, by 1946, there were regular revolts within the army and "Quit India" (Gandhi's movement launched in 1942 that mobilized the nation) graffiti was appearing in army quarters. As Lawrence James mentions in Raj: The Making and Unmaking of British India

The culminative effect of these mutinies was to generate a mood of despodency at the top. The weekly intelligence summary issues on 15 March bleakly admitted that the Indian army was wobbling and 'only day to day estimates of its steadiness' could now be made

Things calmed down later in the year once firm commitments to Indian independence were made.