I use a few of these
The Wednesday one does what you are doing plus also provides tinned and packet goods, cleaning items and pet foods etc. You can take as much or as little as you like. They have a charity can on the counter that you can pop money into if you want. Nobody sees what you put in, and nobody sees if you put in nothing. This one is based in a community centre and a nice hot meal is also available for free as they use some of the donated products.
The Saturday one is the same idea, the donated food is free and you can "buy" extra items that they buy at a cash and carry things like tins, baby items, and cleaning products but I feel these are more expensive than some of the cheap shops but saves you trailing the shops. They charge you per item at a price they have set based on what they paid.
We have a local nursery that works with fareshare and when they get items they just leave them outside for people to take.
If you have overheads to cover then contributions are handy. But as someone who had struggled financially for a few months due to illness and losing my job these places are a godsend and some weeks to have been expected to pay a contribution, even a pound or two would have made it impossible for me to go.
I also pick up from people, ordinary people like you and I, through Olio and it is entirely about saving waste.