I am loving my new double panniers. They are from the Dutch firm Beck, and have loads of capacity (46 litres) and are waterproof.
They have straps to attach them to your rack, and are designed to be left on the bike rather than carried around when off the bike. I’m planning on adding a few cable-ties to secure them to the bike rack, and hopefully stop anyone from stealing them.
I now carry around a backpack when I’m off the bike, and just fling it on one side of the panniers when cycling, and then use the other side for shopping bags or transporting waterproofs.