Good morning! If your loo doesn't have the usual syphon system, then its fitted with either 1) a variflush valve or 2) a flapper valve - both of which can be push button operated. Anyway, both of these valves can fail, which allows water to continue going down the pan, and I guess a replacement is necessary. The likes of B&Q, Wickes and Screwfix do a variety of these things and I recommend that you replace like for like to avoid other issues during installation.
Your loo sounds like it doesn't have the conventional ball cock but it will have an inlet valve of some kind - some of them have rectangular floats, others like plastic umbrellas.
Your loo will have to be split (that is, the cistern removed from the pan) to allow your flush valve to be replaced. Post back if you want some info on this.
John, May 2008