I have accidentally painted MDF and new wood panelling with an undercoat for walls and ceiling’s

Give it a sand and start over. Primers need to be used correctly. Emulsion primer will absorb in to the mdf and not give you a good adhesion base. It's not as bad as it seems though and easily rectified. Hope this helps

Personally I would give the mdf a light rub down using a 120 grade sandpaper. Then apply an oil based undercoat for woodwork. De-nib between coats which is a light rub down to take any bits off. Then finish with your top coat of eggshell. For quickness depending on how much of a proffesional finish you are looking for you could apply another coat of the undercoat you have used. De nib between each coat (rub down). Then apply top coat of eggshell. Thanks. Aaron.

How can you accidentally paint something I've never heard of undercoat for ceilings and walls

as long as you give it all a decent sand down first to key the areas,applying the topcoat is fine