Hi. This sounds like the washer which sits between the cistern and pan has perrished and is not sealing efficiently. These can be replaced, but you will have to isolate and disconnect the water supply, unbolt the cistern from the pan (and possibly unscrew from the wall) and lift the cistern clear. You should then see a large foam rubber washer. Replace this and re-assemble. Put a new washer on the joint where the water feeds into the float valve to be on the safe side.
John the plumber
April 2009