I don't see it as being very likely Britain would support the CS without the US resorting to nigh-on-ASB levels of being a dick.
Any British intervention is more likely to be against the CSA.
A fair fight between Britain and either one of them though just wouldn't be funny.
4 times the UK almost intervened on the CSAs behalf, twice for humanitarian reasons (stop the slaughter and impose a peace that invariably would recognise the CSA), once for honour and finally a French sponsored attempt to bring the British in.
In order these are:
June/July 1861 (wake of 1st Bull Run, stop the war and bring both sides to the table)
December-January 1861/2 (Trent)
September/October 1862 (wake of Antietam, fear of a slave revolt)
June/July 1863 (Private members bill backed by a known Francophile after consulting the French Emperor, withdrawn after Gettysburg)
It was never as simple as "we back the CSA", but rather the British wanted the war over and normality resumed, and for the first two years it looked like the only way of doing that was to back the apparent winning side (CSA).
Picking a PoD for the intervention, Trent is well covered, 1861 would simply be over immediately and 1863 would be Anglo-French. The post-Antietam intervention may well be your best bet.