You could try chemical attack.
Sinks get blocked by a combination of debris, fats and limescale.
Start with BOILING water, straight from the kettle.
Caustic soda will attack the fats. Use this with EXTREME caution. Put this in a cold sink, wear gloves and goggles and WAIT. Make sure it is flushed away properly, using lots of water.
Hydrochloric acid will do for the limescale but whatever else, don't mix it with the caustic!
The various unblockers you can buy from supermarkets are dumbed down beyond usefulness for most serious blockages.