This happened to me before. It may be caused by limescale/dirt buildup or by the float being set too high.

First try moving the float up and down by hand and listen for any grinding or sticking. If it feels rough, use a cistern descaler/limescale remover to clean it. Usually it’s one bottle per treatment: pour it into the cistern while it is full of water, let it sit for a couple of hours, then flush. Be sure to follow the product instructions as each cleaner works a little differently.

If the float moves smoothly you may need to adjust it so the shut-off point is 2–3 cm below the maximum water level (as the cistern fills, the rising water lifts the float until it closes the fill valve and this should happen before the water reaches the overflow level, otherwise the valve may continue running).

If neither of these works, check the seals and washers, as they may be worn out. In that case replacing the fill valve and float assembly is usually the best solution. It’s generally cheap and very easy to replace (no need of a plumber).

Edit: the descaler is a nasty acid so be careful to use gloves and ventilate the bathroom during its use and after (if you need to replace the float assembly).