We are not able to pick up your box and reuse the packaging at the moment, but it is something e are striving to offer in the future. The box itself and most of the packaging ingredients can be recycled along with household goods.
The insulation is made out of recycled PET, which is made from plastic bottles & food trays. You will need to check with your local council if this can be recycled. To find out more about PET take a look at this article.
You can also take a look at recycle now's Recycling Locator to see what you can recycle in your area.