All Courts have the power to award costs or not...

Under the rules of equity if you have acted in honour, good faith and with clean hands and in your pre-action protocol done all that is humanly possible then the rules of equity prevail over the common law which is that the looser pays the winner.

Remember... if you are forced into Court then as:

'no man shall set up his own iniquity as a defence, any more than as a cause of action'

you should not be liable for costs... Montefiori v Montefiori (1762)[2]