Hi Pomst,
If you lift the lid on the cistern you will find the flushing mechanism attached to the handle.
Unfortunately this mechanism has to be removed.
Underneath this is a piece of polythene that enables your toilet to flush, this can be purchased for a few pence from a plumbers merchant or you can make one yourself. You will have to remove this to see what diameter it is.
The job in itself is really quite simple to do, but the water to the cistern has to be turned off, the cistern emptied of water, (flush it with the water off) and then remove the cistern itself by disconnecting the water supply and overflow.
Unscrew the flushing mechanism, this is done by removing the plastic nut from underneath the cistern. You will see the damaged polythene washer that needs to be replaced.
It should take no longer than an hour and cost, at the most �1. If you contact a plumber you are talking at least �40.
Regards