How can I make a toilet cistern fill enough to flush ?

My daughter's rented house has a toilet that will not fill enough to flush. If I top up the water in the cistern from a saucepan, the flush works perfectly,but the filling system is something I've not seen before, it looks like a misshaped ring doughnut with a tube through it with a thin chain or wire linking them at the top.The house is rented, so I can't do anything drastic, but I'd really like to know how it works to be able to fix it.