28th April-4th May but shops often run promos for longer. I think Clean Green Nappy already has 20% off, I don't know if they'll do extra promos during the actual week (quite possibly).
Most nappy shops will have offers and discount codes, or they have in previous years. If there is a particular nappy I want, I tend to google for every UK stockist then compare prices, but if I want several different things I have a look at websites to get a feel for where the best discounts are and then buy in one transaction as it usually works out better for postage. If you want certain brands like bumGenius/Flips, the distributor tends to set the maximum discount so prices will be the same everywhere so free postage will be the thing to look out for.