Broken delivery appointments are a common cause of complaint. For example, you buy some furniture and arrange with the shop to have it delivered on a particular morning. You take time off work on the delivery day, but nobody appears.
One way to give yourself some rights is to make time of the essence when you are buying the goods. When you make the initial contract with the shop, specify that they must be delivered on or by a certain date. Write this date on your receipt and on the order form in the shop. If the time or date is broken you can cancel the contract and claim back the money you have paid.
Even if you have not done this, you are not expected to wait forever for delivery. If your goods do not arrive on the specified day, write to the shop immediately to inform the manager that unless delivery is arranged within a specified period of time, you will cancel the contract.