Do I need to prime kitchen cupboards if they are already painted

No you only need to use primer if the wood is bare. As long as you give it a good sanding and clean it will be fine. If the paint colour is different you're looking at 2 coats not one. If the original paint is oil based eggshell make sure the new one is too otherwise you will need to undercoat it before applying a waterbased eggshell on top of oilbased. Always add a little white spirit to the oil based eggshell so you get a nice smooth finish. Happy painting!

Preparation really is the key to a good paint job,you will still need to apply a primer as you will need your new paint to key to the surface of the doors and units.I would suggest using a product from crown paints called "Grip Extreme" its water based but once applied it will give you a great surface to apply your paint finish to,most people prefer satin finish and make sure its a solvent based one as these are more durable once applied