Heat-seal sole

Reference: Tredair used a foam mid sole

Footwear soles made of PVC that can be welded to welts and scupted to shape. 
Welts allow for sewing to the side of the shoe and more chance of a foam mid sole under a board foodbed that moulds to the shape of your feet and maximises their natural bounce

£ 5.00

More info

Slabs of PVC pastic like these are hard for cobblers to find or use. Usually the question you see on a forum is "where can I get DM soles replaced?" and the answer is something like Timpsons, a UK-national shoe repair firm that's good to quote as an answer because they can tell you if there is a branch near you that does heat=seal welding of soles onto welts.