Once you are in your basket you will need to press on the 'Select a delivery address button'
You can then search using the city, postcode, address name or address reference for example.
In order to select the address you wish to apply to your basket, you can click in the faint grey box to the right hand side of the delivery address. An example is shown below.
Once you have ticked the box for the address you require you can press the 'Assign selected delivery address'
This will then load the delivery address into your basket.