After looking at the ingredients in your moisturiser, you should check out the label on your daily facial cleanser. Certain cleansers can strip the skin of necessary oils while cleansing impurities and toxins from your skin. Check to make sure your cleanser does not have salicylic or glycolic acids, as these ingredients can be too harsh for those with very dry skin.
I love my glycolic face wash, but I try to use it every other day and use a creamy cleanser on my off days to avoid drying out my skin. Look for cleansers that are moisturising and soap-free for best results. My latest favourite is the It Cosmetics Confidence in a Cleanser (£24). This makeup-removing formula is anti-ageing, hydrating, and soothing, leaving your skin feeling baby soft.