People do need a referral to use a food bank. I would guess people use the one most convenient for them. My understanding is that this is donated food with a reasonable shelf life. People receive enough "emergency supplies" for a few days and can only receive one parcel every few weeks.
However, there are other places, such as the community fridge mentioned by Callistemon. I've been using one for the last few weeks. This is mainly supermarket surplus and there's usually veg, bread, fruit and some meat. The rule is that we're allowed one bag and are repeatedly asked only to take what we can use over the next few days. Everybody is very civilised, waits in queue and we swap recipes. Most people arrive on foot and are locals, but some people come from the surrounding villages. There's free coffee/tea and cake if people want to stay and chat.
There's also Olio, which people can use to give away free stuff, including food.