Hi XXXXXX XXXX;
The white stuff is called effloressence. It is from the salts in the masonry being leached out by the water incursion.
Unfortunatly there is no easy or cheap way to remidy this. You need to stop the water from the exterior of the basement.
This can be done by trenching around the building and laying in a french drain, or by excavateing the soil away from the masonry and applying a water proof barrier against the basement walls.
Best, THS
Jack of all trades Master of a few.
#1 Home Improvement Expert. Over 30 years experience in construction, and home repairs