And, one can argue from fact, slavery in the US wouldn't have lasted as long as it did if owners of fabric mills in England hadn't profited from it.

One can, but its a foolish argument if it assumes that the South would have voluntarily given up slavery - especially before 1861 - if not for British cotton manufacturers.

It also ignores the fact that although "cotton was king", slave labor in the south produced a wide range of commodities, from sugar, rice & tobacco to lumber and pitch and turpentine.

One could just as easily argue that the British manufacturers acted as capitalists everywhere ALWAYS do, war or no war: minimize costs and maximize profits. Greed is the motivating force of capitalism.

So, no - the Civil War can't be blamed on Britain.