How union with Britain might accelerate American industry

Would Britain allow North America to industrialize if the colonies remained inside the United Kingdom?

Yes; political integration and easier access to London finance could make North American industrialization faster rather than slower.

Britain could not easily prevent North American industrialization and would gain from encouraging it. Keeping the territory within one state would require political integration, perhaps through a greatly enlarged Parliament or even another chamber. Direct access to London's capital markets could also accelerate development. Lenders operating under the same legal system would have clearer judicial recourse, reducing risk and making investment more attractive.