How can I control water in my basement without a sump pump?
Permanent sump pumps are a common feature of homes in the U.S. Perforated piping, or "drain tile" (a reference to archaic techniques) remains in place below the concrete slab, usually embedded in washed rock. The sump pail is located in a utility room and the pump runs as needed, often year-round. 

You'll need to build such a system and leave it in place, or you'll need to divert the water outside the home, perhaps using a "French drain" (gravity-driven) piping system.