A friend of mine had a cardboard coffin, but it looked very sturdy and stylish, with a tasteful oak veneer finish on the outside.
The friend had a woodland burial, and I'm told cardboard coffins (and probably whicker now) are the norm for this, as the material decomposes more quickly. I didn't go to the burial, only the church service, but I'm told woodland burials are shallower than standard burials as a shallower grave allows more oxygen to enter the coffin and thus helps the remains to decompose more quickly.