No different rule for pigs, in any event you can be fined if you let your pigs contaminate a steam such that it causes damage to the wildlife in the stream, either animal and vegetable (a legal case would be likely to be brought by Defra following a complaint), and can be sued if your negligence if letting your pigs contaminate water causes harm to a user of the stream or his enjoyment of the stream further down.
Having said that an accidental fowling following an escape is unlikely to cause any damage - eg one poo or a pee would not damage any running water.
Pigs are good swimmers and will happily wade off up or downstream, or just cross it to freedom, so yes electric fence before it to prevent this, and train your pigs to the fence first.
I would not wish to be a possible pollutant, but equally I would want to be sure that I was not poisoning my pigs from something that someone else upstream had contaminated with - accidental agricultural spill of pesticide for instance.
For these three reasons (upstream contamination, me contaminating downstream and pigs escaping) streams are in our view not a good mix with pigs.