Peeling paint

[Brushieblue]

Does anyone know the best way to deal with peeling paint We want to paint our kitchen but the paint that was under the wallpaper is like a thick skin (Dulux Kitchens and Bathrooms paint) that is peeling off, we've tried sanding it down, but its still peeling. Is there any sort of paint we can overpaint it with, as we dont want to re-wallpaper and we just want to paint it but have a nice finish?