Who did the british fight in the civil war?

They came close to fighting the Union, after the US Navy fired across the bows of a British mail-ship carrying two Confederate envoys to Europe. (Interestingly, the violent disagreement was resolved by the dying Prince Albert at Windsor, by editing the message that the Foreign Office was due to send to Lincoln's Secreary of State.)

After that, the British did build blockade-runners to aid the Confederates, but after the Emancipation Proclamation, they could not do this openly without looking pro-slavery.