If you are confident the leak is sorted out (which i would not be... judging by the pics) .
Leave it a month or so for the salts to stop moving about and the wood/tiles/bricks to dry out. Then clean with an "Efflorescence remover" available from builders yards and all the big sheds. I would try this on a small area first ..to make sure it does not alter the appearance of the brick (other than removing the salt).
You could then apply a impregnating sealer to stop the ingress of water into the brick work (optional but worth while).Tests are proving that these sealers help prevent freeze/thaw damage and heating bills are reduced.They will also help stop the calcium carbonate trying to escape but while letting the moisture out.
Don't seal straight away make sure the damp problem is corrected first!