Constant voltage charging is OK for lead-acid batteries - as long as the voltage is set to the correct value.The LED sort of helps with that, taking an increasing amount of the total current as the cells charge. You may want to see what the actual battery charge current is at "full charge". Then compare that to the battery capacity and chemistry. It might be OK. If you need a better charger, you'll need a bit more circuitry to avoid overcharge.
You might consider a cheap DC-DC converter off e-bay. It'll only give you a constant voltage, but that is likely superior to the constant current strategy.
Constant voltage charging for Ni-Mh or Ni-Cd batteries is a seriously bad idea!