Different parts of British society held sympathies for both sides.
The South thought that Britain and other European Countries would become allies because of the cotton supply (most of the worlds cotton at that time was grown in the American southern states). So the Confederacy made strong representations to Britain. This came to a head with the Trent Affair and Britain came close to joining the war on the side of the Confederacy. If Britain had joined the Civil war on the side of the South then this would have been directed via Canada and the North would then have to fight on two fronts. The North was obviously keen to avoid this and the Trent Affair was resolved, but Britain was always seen as favouring the South.
When the Alabama was sunk off of Cherbourg survivors were picked up by the Britsh owned 'Deerhound' rather than being left to be taken prisoner by the Kearsarge giving further cause to see Britain as sympathetic to the South.