The Industrial Revolution started in the mid-18th century in England. The steam engine was introduced before the Seven Years' War (1756-63), where England and its allies won and the former essentially became the sole European power in India, though it still only controlled a small fraction of the territory. The Industrial Revolution was well underway before the Anglo-Mysore and Anglo-Maratha wars where England gained control of most of India. The Scramble for Africa was 100 years later. The American colonies were confined on the east side of the Appalachians. The amount of revenue derived from control of that amount of territory couldn't possibly have driven the largest economic transformation in the history of the world. Many empires of similar size have come and gone with no similar jump in the world economy.
>In 1750 Britain imported 2.5 million pounds of raw cotton, most of which was spun and woven by cottage industry in Lancashire. The work was done by hand in workers' homes or occasionally in master weavers' shops. In 1787 raw cotton consumption was 22 million pounds, most of which was cleaned, carded, and spun on machines.
What could have contributed to the Industrial Revolution, however, is the technology of Bengal, the first region of India that England gained control of. The economy of early-18th-century Bengal has been described as proto-industrial. The lazy "anti-imperialist" critique of the Industrial Revolution in fact undersells India as merely a source of resources. In fact, in the Anglo-Mysore wars, it was the Indians who had superior artillery (though English tactics carried the day) — designs adapted from the "Mysore rockets" were used in the siege of Baltimore, which gave us the infamous line "the rockets' red glare" in that song where they almost seem like an anachronism.