My own experience at the time, was that tins of cream for my morning coffee, gradually disappeared from the shelves. I/we normally keep a fair stock of anything which is used regularly, and which will keep, so we had plenty of stock in the pantry. It became a case of looking for it, and restocking when they had it on the shelf. Other than that, there were no shortages we suffered at all.
All shops and supermarkets do occasionally suffer shortages, of individual items, that is perfectly normal. I've at times been in Lidl, when they have run out of milk, or a certain dog food - it doesn't indicate a national shortage, just a minor local supply hiccup.