If it's old it's bound to be worn.
The water obviouly is running into the toilet pan or you'd have a wet floor. Your diaphragm in the flush unit has punctured or disintergrated. You wil have to remove the flush unit. Turn off the water feed to the tank [cistern] Remove the float arm from the feed valve by removing the retaining split pin, observe how it's fitted, [Brass one] Remove the syphon arm from the flush handle. Mop out the water in the tank [cistern] then undo the large nut under the cistern, I'm assuming it's not a close coupled one. then undo the large nut that holds the flush unit in the tank. keep the rubber seal/s.
Remove the flush unit and replace it with a new one don't bother with the diaphragm membrane as I've had trouble in the past getting one so it's quicker to replace them with ones you don't have to remove to replace the diaphragm.
Remember when re-assembling the flush unit put the seal and large nut on the flush unit then fit the flush pipe [make sure it's securing nut is on the pipe] into the flush unit make sure it's a good fit on the back of the toilet. Then tighten the flush unit nut, followed by the flush pipe nut. Fit the flush unit arm to the flush handle then refit the float arm to the valve bracket. Make sure the float arm rides free up and down. Turn you water feed back on. watch it fill to its proper level and hey ho!! away ya go and flush that loo!!!!!
bob, February 2005