Short answer:
You have to be a little careful there with terms. You have to be precise about which force you're speaking of, and whichever force you might speak of, there was no "average member". To know what someone might have sounded like, you'd have to be precise about just who you're speaking of, born where, of what class and so on.
Discussion:
The "British Indian Army" was an Army composed largely of local people from India, many of them Muslims. The "British Army in India" were regular British Army units posted to India. The collective of these two forces would be called "The Army of India"
In all cases you have a variety of accents, and in some cases a variety of languages. British soldiers' accents varied substantially by region of origin in Britain; and officers and men had substantially different accents as well. Similarly, local soldiers themselves have no one accent-- India is a very big place (and British India was substantially bigger than today's nation, including many ethnicities no longer with the post -1947 borders. They had many different styles of speech, and indeed different languages. Sikhs would have sounded very different from Gurkhas, and the Corps of Guides raised from the Punjab would have been different again. After the Indian Rebellion of 1857 (aka "The Mutiny"), the British substantially preferred Muslim and other North Indian soldiers over Hindus.
As an example of the variety of accents among just soldiers born in the British Isles, you could listen to recordings made by a Wilhelm Doegen German linguist of British prisoners of war during WW I; he recorded many different regional accents. While these differences had diminished substantially by the time of the Second World War, they're an indication of just how varied English accents were. While we don't have similar recordings of Indian soldiers from the early 20th century, there's no reason to think that their accents would have been any less varied.
Sources:
Berliner Lautarchiv British & Commonwealth recordings
Ellinwood, Dewitt C. “ETHNIC ASPECTS OF THE INDIAN ARMY IN WORLD WAR I.” Proceedings of the Indian History Congress, vol. 39, 1978, pp. 823–831.,
Barkawi, Tarak. “Culture and Combat in the Colonies: The Indian Army in the Second World War.” Journal of Contemporary History, vol. 41, no. 2, 2006, pp. 325–355.
Khalidi, Omar. “Ethnic Group Recruitment in the Indian Army: The Contrasting Cases of Sikhs, Muslims, Gurkhas and Others.” Pacific Affairs, vol. 74, no. 4, 2001, pp. 529–552.
ROY, KAUSHIK. “Discipline and Morale of the African, British and Indian Army Units in Burma and India during World War II: July 1943 to August 1945.” Modern Asian Studies, vol. 44, no. 6, 2010, pp. 1255–1282.