My re-usable supermarket bags are chock full of plastic bags. If you get those double packs of Griffins Chocolate Chippies, you get two plastic trays, individually wrapped, with a third bag encircling the lot!
A lot of these 'soft plastics' are now recyclable at the supermarket. But it would be better to eliminate them.
The soft plastic recycling include the multi-use plastic bags, so no different.