sounds like you live in a low pressure water area where the incoming supply fill's a water tank up in the loft, when you have no water remove the tank lid and check inside that the float arm is not sticking ,check that the cotter pin is free(not seized) , this should then allow the arm to drop and water to enter the header tank.if water still enters slowly there maybe rubbish.(A piece of grit entered the pipe due a main's repair nearby) blocking the incoming valve,with the water turned the valve will need to be stripped while down change the ball cock rubber that fits in the shuttle then reassemble the parts and check that the water shuts off before reaching the height of the overflow pipe .
wirecutterman
June 2009