There will be two things in the cistern you should check:
1) The flap at the bottom. If it's not seating correctly, it will cause a continous run.
2) The floating mechanism that shuts the water off when it floats high enough. There's an open pipe sticking up about 2/3 of the way that catches "overflow." If the floating switch does not turn the valve off, the water will continuously run and drain into this pipe. The floating mechanisms come in several forms, but they all involve a large floating ball of some sort attached to a switch of some sort. All you need to do is adjust the floating ball so that it sits about half a centimeter lower.