Advice From Your Local Plumbers (Croydon)

If a plunger is not able to eliminate a blockage, try and get hold of a plumber's snake AKA spiral cleaner.  They are available in most hardware stores.  Disconnect the blocked drain pipe from the trap, and feed the wire into the pipe. When contact is made with the obstruction, turn the handle of the snake to rotate the spiral.  Usually, the spiral will break up the obstruction.

Sometimes, it is not possible to remove an obstruction from the sink end.  If the waste pipe discharges into a gully, try pushing a garden hose up the pipe from outside.  This in itself might do the trick, but more often than not you will need to turn the tap on to move the obstruction.

When you are unable to clear a blocked waste pipe from either end, you will have to try and take the bottle trap apart.  Place a bucket under the trap before dismantling it, and put a plug in the sink's plug-hole.  When you have removed the blockage from the trap, rinse it out and reassemble.

If the drain pipe is blocked by fat or coagulated oil, a bit of heat could melt the fat and send it on its way. You can use a portable heater to warm a waste pipe just where it bends.  You should soon notice the blocked up sink begin to go down.  Eliminate all traces of fat by turning on the hot water tap, and leave it running for a full minute.  Job done :-)