Cardboard boxes can be collapsed down and disposed of in your yellow bin. Cardboard items such as cereal boxes (with the insert removed), tissue boxes, and paper roll inserts can be disposed of in the yellow bin. Bulk qunatities can be taked to CWMC (recycling voucher or charge applies).
Hint: Larger cardboard boxes in good condition are always sought after by people moving or who need to store items. Check local online community groups to see if anyone wants them.