Modern toilet flushes don’t use a large float (ball cock) to close the valve when the water level in the cistern tank is reached. They use a diaphragm type washer that uses the water pressure to help close the valve. These have a small hole in them to allow water to a small control float which changes the pressure either side of the diaphragm; this moves the diaphragm opening or closing the valve. If the diaphragm splits, the pressure will be the same on both sides and the valve will not open to fill water cistern, the only water going though the valve will have to go through the small hole that goes to the control float, so will take a very long time to fill the cistern, if you look you will see a small jet of water near the float.
The diaphragm/washer is easy to replace turn water off, flush toilet, undo plastic nut see picture and replace diaphragm, make sure to line up any alignment lugs when refitting.
Turn water back on, check valve turns off when water level mark is reached on the cistern, if not you can adjust the level up or down with the adjusting nuts on the float.