How to fix a cistern float that jams
A new fill valve costs about $10, so it's probably more cost effective to simply replace it.
Procedure


Turn off the water to the toilet using the shutoff valve
Hold the flush lever on the toilet down (not pictured), until nearly all the water has drained from the tank.
Remove the supply line from the fill valve, by turning the nut anticlockwise.
Place a bucket under the fill valve (where you just removed the supply line from).
Remove the retaining nut from the fill valve, by turning it anticlockwise.



Remove the refill tube from the overflow tube.
Lift the fill valve out of the tank.

Installation

Follow the installation instructions included with the new fill valve.