[IronJack]

Great Britain would never ally itself with a country with the institution of slavery

They would if it meant preventing the collapse of their domestic textile industry, whose plants were fed with Southern cotton. However, since they had developed alternative sources and an alliance with the Confederacy probably meant war with France (among others), they wisely thought they'd wait it out to see a winner emerge. When Meade stopped Lee at Gettysburg and Lincoln announced Emancipation, the decision was made for them. Now they could hide their commercial reluctance behind a moral mask and remain above the fray.

[rockrr]

The most likely reason for any British alliance with the confeds would be so that they could stage their troops more conveniently for their next conquest.

[Kartographer]

You answered the question: "However, since they had developed alternative sources.."

Developing alternative sources would in the long run be much cheaper than helping in a war to protect something that they had already spent treasure and blood in fighting against.