I've managed to get free next day delivery (inc sat and sun) with this neat little trick. Check out as normal and select a free day for delivery, in my case when I ordered yesterday I selected Tuesday as sat and sun were £14.99
Pay for goods and complete the checkout. Phone up ao.com customer service number from the phone number you entered on the order and choose the option to reschedule the delivery. Select the next option to deliver the goods earlier. The automated system will offer you the earliest day for delivery which is almost always next day. Confirm that you would like to change the delivery to that day. The system will confirm the change and send you an email.
To check it has worked track your order on the website and you will see instantly that the delivery has been changed to the next day for free.
Just a little tip to beat the system.