I have always tried to get them to spin rather than knock them through or out. Give one side a wack so that core plug rotates in its seat. The side that rotates out can then be grabbed with some mole grips and pulled out.
I just used a screw driver. You want to try and get it as far over one side as you can before hammering. I get them to spin in/out of the block not wind them in and wind them out. Hope this makes sense
Punch a hole in the middle with a sharp pin punch or spiker,(relieves the surface pressure used when it is installed) then gently lever out with a strong screwdriver in the hole you have punched. Seal new with Wellseal or whatever, and peen the centre of the new plug with the ball end of a 1/2 lb. ball -pein hammer.