Hi Roz, First, it is very important to establish whether the veneer is real wood pine or a printed melamine. They can be very difficult to tell apart as the modern photo laminates are very good (most laminate floors are photo melamine but look just like the real thing).
How to tell:
Is the surface embossed with a wood grain texture? Look very closely (use a magnifying glass if necessary). Does the embossing precisely match the wood grain Or does it bear no relation to the wood colouring? If it matches exactly then you have a real wood veneer. If there is no match it is melamine.
Does the veneer splinter? Find somewhere not visible to test this. Melamine will not splinter real wood veneer will.
If your wardrobes have a real wood veneer I would suggest an oil based undercoat (check on the tin that it says 'clean brushes in white spirit'). Wash the wardrobes with sugar soap to remove grease and grime (please don't be offended but it's always there even if you can't see it and paint won't stick to a greasy surface). After washing, sand the surface with 120 or 150 grit silicone carbide or aluminium oxide paper (both have a grey sanding surface). Wipe with a damp cloth to remove dust and allow to dry. It is important to sand the surface evenly before painting to provide a good key for the paint to stick to.
Two coats of undercoat will usually cover the colour underneath. Then you can apply whatever decorative finish you desire using either acrylic paint or oil based. I prefer oil based as it is more durable and easier to clean.
If your wardrobe has a melamine veneer you will still need to wash and sand it as described above. Then use a melamine primer for the first coat of paint. Melamine primer is available in most DIY or paint stores. It is specially formulated to stick to plastic (melamine). Decorative finish as above.
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Screwmaster
March 2011