Either:
1) The washer in the ball valve has begun to perish, and is letting water through - Solution: Replace washer - Cost: 50p.
2) The ball valve has a hole in it and is taking water, in this case the ball itself need replacing.
3) The other thing it could be is that the level the ball valve floats at is slightly higher than the overflow outlet, and it is constantly trying to fill it to that level but it always runs out of the overflow. To stop this adjust the level the ball floats at.