Did the British fight in the Civil War?

Yes they did but not in the American one, in the British one. The only involvement in the American one was trade, running arms and "luxury" goods through the blockades for the South. However attempts to involve it in the war though the cotton trade failed as there were alternative supplies through the British Empire and it was trading corn with the North. The CSS Alabama was built secretly by a British shipyard for the South capturing 60+ "prizes" during it's history.