The only reason Sainsburys hasn't had contactless turned on until now is because its current POS software doesn't support it. They've been having trouble over the last year or two getting the updated POS software onto some of its more rural stores.I think they've rolled out contactless ready terminals to all stores. They are Ingenico iPP300 series terminals.
The Asda stores I use have the same terminals but the same cannot be said for Tesco which still has old terminals.
The current software is pretty useless. It even has trouble with Chip and Signature cards in some stores where you can't remove the card until the Yes the signature matches button has been pressed (Otherwise the transaction cancels). Kind of impossible to verify the signature if the card is in the terminal!