Agreed. It's also true that the early Industrial Revolution cotton mills used slave-picked cotton, because although millions of slaves continued to exist and their produce was imported even after slavery itself was banned in Britain, slave labour couldn't possibly compete with industrial mills in output of finished goods. (And not just because the early mill workers often earned little more than the cost of procuring, securing and covering the subsistence of slaves)

The UK had the tech to build mills and the financial system to fund the capital costs of building them though (and a larger, more global market to sell mass produced cotton to)