Just bear in mind that if your box is damaged, BA may not be so willing to compensate you as it would if your suitcase was damaged.
Cardboard boxes are not designed to run down airport conveyors, through x-rays and other security screening apparatus and then be loaded in ULDs or as bulk.
So if your box gets torn as it trundles down a conveyor and your items spill out, BA may not pay out if you then try and open a Damaged Property Report (DPR) and may try and say that a cardboard box is unsatisfactory as baggage.
That said, I have travelled numerous times on BA and other airlines with boxes without problem but one should try and ensure they are sturdy and shrink wrapped to survive the journey.
Routes into Africa often see many pax checking in poorly prepared boxes or very cheap disposable bags and then getting upset when their baggage arrives damaged!