This is a subject filed under "interesting and should read up on it someday" so, as much for myself as for Stone, I did a quick search to find a relevant paper with a literature review that would provide some suitable starting points. This 2023 paper "Slavery and the British Industrial Revolution" -
https://www.princeton.edu/~reddings/papers/SBIR_Paper.pdf - does that, how well I can't comment but I'm assuming it's up to scratch and it includes the two sources Andy gave above. It also gives a good insight as to how some quantitative estimates of the effects of slavery (or other events) can be calculated.
The paper attempts to assess the impact of slavery on the British economy up until abolition in 1833. The technical bits of the paper are complicated but the idea is standard in modern empirical economics. It's just a "natural experiment" - the authors have looked for a source of random variation that separates otherwise very similar slave traders, in order to isolate the causal effects of their slave trading activities. In this case that variation is time spent sailing across the Atlantic, as more time at sea tended to kill slaves and reduce the profitability of the venture. They then connect data about each voyage's backers to different parts of the UK and do a bunch of stuff to try and firm up casuality (excuse the handwaving explanation) and find:
"Using only data up to the 1830s, we show that exogenous increases in slavery wealth in the preceding period are strongly correlated with a lower agricultural employment share, a higher manufacturing employment share, more cotton mills, and higher property values at the time of abolition."
They then try estimate some aggregate effects on the entire British economy:
"We use the model to calculate a counterfactual in which we assume that Britain had no involvement in slavery. Comparing actual levels of economic activity in 1833 to those in this counterfactual, we find that slavery wealth raises national income by around 3.5 percent, which corresponds to a decade of growth in income per capita at the time. For the locations within Britain with the greatest involvement in slavery, total income increases by more than 40 percent. The model also suggests that slavery had important implications for the distribution of income: in the most exposed locations, capital owners’ income rises by more than 100 percent, and the income of landowners falls by around 7 percent. Workers, on average, benefit from the industrial development induced and accelerated by slave wealth.
"Our results do not suggest that slavery was essential for Britain’s industrialization; nor do they demonstrate that its effects were largely irrelevant. Instead, our quantitative results mark a middle ground, with slavery significantly accelerating growth and structural change at the height of the Indusrial Revolution. The largest impact, according to our model, is on
the geography of economic activity and the distribution of income, with towns and cities that are exposed to slave wealth growing faster. As a result, slavery wealth shifted the locus of economic activity to the North and West of the country, and it boosted the income of capitalists and workers at the expense of landowners."
I can think of some obvious criticisms, eg slave-trading and slaveholding might not be as linked as the authors claim, or that there are other obvious reasons for manufacturing industry to be based in the north and west of England which aren't accounted for in this model. It includes a counterfactual, economists love them but ymmv. There may well be more sophisticated criticisms of their approach but my econometric skills really aren't good enough to begin making those. And of course this is just one paper - but its findings of "important but not decisive" matched my priors, as the argument that slavery didn't cause industrialisation elsewhere carries a reasonable amount of weight for me.
If anyone is interested in the intellectual background of the kind of causal estimations occuring here, then maybe the Nobel acceptance speech of of Joshua Angrist, one of its key developers, might be worth a read:
https://www.nobelprize.org/uploads/2021/10/advanced-economicsciencesprize2021.pdfAlso Stone, if you're interested in modern policy implications, surely it would be better to read up on Taiwan, South Korea and Poland, all of which have become developed countries very recently?