With reference to the research of economist Utsa Patnaik, who has calculated that over the British colonial periods in India from 1765 to 1938 they took some $45 trillion dollars, given the sizeable total sum and how it was used to fund colonial and imperial efforts, and the movement of Governors and Viceroys throughout the Empire (such as James Bruce, 8th Earl of Elgin), it stands to reason that this model was employed elsewhere in the Empire. (Source)
What evidence exists to suggest use to this kind of system in other parts of the Empire?
And, assuming this was being done in at least some colonies, what kind of figures are we talking about?
So this claim has definitely been making the rounds, and is super controversial. I honestly don't have the standing in Indian history to comment one way or another, but I do want to quote from an interview with Utsa Patnaik that that Al Jazeera piece links to when they mention the $45 trillion:
"Between 1765 and 1938, the drain amounted to £9.2 trillion (equal to $45 trillion), taking India’s export surplus earnings as the measure, and compounding it at a 5% rate of interest. Indians were never credited with their own gold and forex earnings. Instead, the local producers here were ‘paid’ the rupee equivalent out of the budget—something you’d never find in any independent country. The ‘drain’ varied between 26-36% of the central government budget. It would obviously have made an enormous difference if India’s huge international earnings had been retained within the country. India would have been far more developed, with much better health and social welfare indicators. There was virtually no increase in per capita income between 1900 and 1946, even though India registered the second largest export surplus earnings in the world for three decades before 1929."
To phrase it a different way, what Patnaik is saying is that the British East India Company and British colonial government after 1857 used local tax revenues (rather than gold or foreign exchange) to buy Indian exports for British use, and that if these funds had instead been invested at a 5% annual interest they would now be equal to $45 trillion. So it's a more complex and nuanced argument that gets flattened in headlines and social media to "the British stole $45 trillion."