Water proofing the bathroom floors and walls need to be done in several layers during construction to ensure long lasting solution. Other wise , water seepage would be constant , some are visible like yours and some are non visible. There is already lot of discussions happened on waterproofing Bath Area. Check this post .
http://www.mybdasites.com/viewtopic.php?f=36&t=7050
Water could seep through the capillaries around the drain pipe, From the gaps between tiles in walls and floor etc. For your case you have several options with varying durability, cost depends on the type you choose .
option 1 (Long lasting permanent solution) : Remove all the floor and wall tiles (up to 3 ft) , remove screed and follow the post above and treat it like a new construction, relay the tiles after proper water proof treatment.
Option2 : (Regrouting) : This is only effective if floor and wall tiles in bathroom are spaced by few mm apart, so that you can remove the white cement grout and re grout them with epoxy for water tightness. if there is no spacing between tiles, you cannot re grout.
Option 3 : (Water proof Sealing, Temporary may last only a year) : Allow the bath room to dry completely ,remove all the dirt around the grout joints, apply water proofing sealer with a brush on the walls and floor joints. Natural Water proofing sealer is available with Sika , Ardex endura , Laticrete .