The peeling could be caused by a film of grease/dust/dirt on the old paint. Matt is particularly susceptible to this.
You need to clean the walls with sugar soap before re-painting. Sugar soap is available in DIY and hardware stores either as a liquid or powder - it's not expensive and it goes a long way so you only need a small bottle or packet.
Dilute according to the instructions on the packet/bottle. Wash the walls using a sponge or cloth - don't over wet the walls. Rinse the walls with fresh, clean water and a cloth or sponge - again not too much water. You will see how much brighter the walls will look after cleaning - just goes to show how grubby/greasy they were.
Allow the walls to dry out fully (at least 24 hours) and then re paint.
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Screwmaster
March 2011