I don't know about the history of textiles and their development, but didn't the English invent a synthetic cotton process around 1863 that suddenly left a lot of Southern cotton crops rotting on shipping wharves? If this is true, it may have further diminished the attractiveness of getting involved more directly since their economic interests were less pressured at that point.

Also, I don't think the slavery issue can be ignored because of England's own long struggle to outlaw the practice led by William Wilberforce and others. Directly supporting the slavery-favorable govt of the Southern Confederacy may well have been construed as "politically incorrect" in the Parliament of those times, their hatred of the Lincoln administration notwithstanding.