There are many different coffins and shrouds available. If you are using a Funeral Director they will be able to help you source these. If you are looking to source your own, or looking for somethng different, here are some that will supply direct to the public. The Natural Death Centre has a more comprehensive national list on their website.
ecologicalcoffins.co.uk – beautiful, locally made (near Cardigan) wooden coffins made of recycled wood. Suitable for burial or cremation.
bellacouche – beautiful (handmade in Devon ) woolen felted shrouds and coffin covers.
pentiddy shrouds – beautiful woolen shrouds, woven in Cornwall on a peg loom with handmade wooden toggles on a hazel wooden hurdle.
lilywillowcoffins.co.uk – handmade in Wales with UK sourced willow.
cardboard coffin company sell a variety of cardboard coffins, acredited for cremation and burial.
creative coffins – cardboard coffins with a personalised printed design
Please note that I am not personally endorsing any products or affiliated to any suppliers, I am just signposting you to some products that I am aware of. There are many other suppliers which you can search online.