“But given that Europe, primarily England, consumed the bulk of the South’s cotton then how did the North find an adequate alternate source and the UK didn’t?”
England did. When cotton exports from America were greatly restricted due to the Union blockades, England turned to Egypt and the Caribbean for its cotton needs. Also, some cotton shipments from the South still did manage to run the blockades, but only a fraction of what it had previously shipped.
Not nearly enough, though. And even with the blockade runners and supplies from Egypt and India the British textile industry was in a depression for the duration of the rebellion.
But we still have the conflicting stories between you and 4CJ. He says that the Union tariff income rose trying to replace that which they could no longer get from the South. You said that there wasn't enough demand for Southern goods in the North to make it a profitable market for them. So which is it?