It is sometimes thought that the “Fairy Hole’ caves of Weardale are named because of these pale creatures in the waters of this cave system.

White fish such as this one spotted in the Fairy Hole this past summer, are actually very pale in colour rather than ‘white’. There are ‘cave fishes’ that are ‘white’ due to evolutionary pigment loss. The ones in Weardale, and those often spotted in Yorkshire cave streams, are pale due to a physiological reaction to darkness.
Being very technical for a moment: “Melanin pigment resides in cells termed melanophores and it may be distributed throughout the cell, resulting in a dark looking fish, or concentrated into the centre resulting in a pale animal.” All brown trout examined (found in UK caves) have been in the latter condition.
It is most likely that the fish in the Fairy Hole caves have somehow drifted downstream, perhaps pulled in a flood period: it is possible they may have travelled upstream but less likely in as much as is known of the cave system.
There are lots of different underground fishes, all around the world. If you want to know more this website is a good place to start.