If the waster is constantly filling the cistern as you say then it must be overflowing - either into the WC pan or outside.
The inlet valve suffers from two problems - either the "rubber" seal perishes inside the valve and should be replaced or - more usually - the inlet valve merely needs to be adjusted. This can be achieved either by lowering the float into the water (to shut the valve off sooner) or most often by turning the little nylon adjusting screw in towards the valve - and doing up the locknut - It's a rare thing to need to replace the whole inlet valve assembly.
Good luck...
Peccavi
January 2010