Bedding: pillows, duvets, blankets
Blankets and sheets
Some branches of IKEA will accept old blankets and sheets (as well as curtains). They'll give away what they can to charities and the rest will be recycled. So far the only branch we have confirmed is the Cardiff IKEA.
Pillows aren't currently recyclable and most charity shops won't accept them to sell to humans. But some pet shelters will take old pillows (and duvets) for animal use.
Oxfordshire: the Oxfordshire Animal Sanctuary will accept old pillows for animal use. But you can no longer drop items off in the shops - you have to drop them at the animal sanctuary itself in Stadhampton. And they're not currently in urgent need of any bedding: "The dogs are quite comfy at the moment." Source: phone call, January 2018.