Where we are we're lucky to have two small shops (mini versions of larger brands, including the 'well-known freezer food shop'!) within a 2 minute walk of the house, and an extensive farm shop-type shop a 5 minute drive away.
We do have 'large' supermarkets, but no one here does delivery or click-and-collect normally (not on the mainland) so people have had no choice but to go to the shops themselves, or get someone to go for them. But the 'large' supermarkets are usually the ones with the queues to get in, so we've been making do with the ones we can walk to/drive to easily from our house.
And, to be honest, we're doing ok with those. We produce our own milk* (don't import from the UK), so no shortages of that, and we have our own local bakeries (although if you're after something more 'niche' or have a restricted diet in terms of bread, as one of us in the house does, that's more tricky). We also have a reasonable supply of locally-grown veg (especially if you like potatoes, carrots, onions and cauliflowers!)
To be honest, either than having to consider lunches for everyone, and planning ahead a bit more than usual, we've pretty much been eating what we'd normally eat anyway, other than things like pasta and the odd tinned food stuffs. There was a bit of 'storage buying' (rather than 'panic buying') at first, but that settled down very quickly.
I know that's luckier than many right now. I can't even begin to imagine the stress people on the mainland have been through (especially when essential workers/NHS staff were faced with nothing but bare shelves) when it comes to just feeding themselves. And as for the pictures of all the uneaten food in bins... those people should be ashamed of depriving others of perfectly good food just because they had the time and money to over-buy, but were never going to eat. 
- Re the milk shortages in the UK - boy, have I learned a lot about cows' milk! In terms of cow's milk, we have 'yellow' full fat milk (the creamy, sweet kind of fresh milk you make rice puddings out of!), 'green' whole milk (3.8/4% fat), 'blue' semi-skimmed (1% fat) 'orange' skimmed (0.1% fat) and 'red' milk, which is lactose-free. Whereas some of the colours seem to be reversed in the UK, your semi-skimmed has a higher % of fat, and you have 'orange' milk which is also called '1% milk'! And that's without all the 'BOB' milks (I had to google that!) and other treated cow's milk products! Who knew milk could be so confusing!
