Hi mandie73 Sounds like you have Diaphragm troubles thats not so easy to cure it means turning water off remove ball valve and hand lever with linkage any water left in the cistern then undo the large flush pipe connector nut and removing the big plunger/diaphagm chamber the plunger should drop out at this stage to reveal a large plastic diaphragm that is torn with holes that is what needs replacing if you have some thickish polythene you should be able to make one as old pattern (minus the tears or holes) then put it all back together in reverse re-adjust ball valve to allow it to fill to water levels HTH Tez
I had the same problem as you and as tezestwing says, it was the diaphragm. I phoned an odd job man out of the local paper and he fixed it for me for �20. I bought the replacement part myself for a tenner from B&Q.
If its an old one it may be pre-diaphragm. In which case it is perhaps ball-valve. You just adjust the arm attached to the ball so the level fills up more before the water supply cuts off. Bend the arm upwards slightly if necessary.