In the UK, does the rate of annual price increases in food consistently beat inflation? How can we tell? Informally, I've often seen it claimed that the price of food always goes up. Certainly, I do notice when the price of my £5 food bag goes up 50p or when my £1 milk goes up 20p. Yet, whenever I've asked those with an interest in economics why they aren't investing in stockpiles of food, they laugh and tell me that doing so would be to bet against human prosperity and that over time, the price of food goes down. Clearly, both side cannot be correct. I've tried to look in to this on my own, for example I've tried to use the data available at https://tradingeconomics.com/united-kingdom/food-inflation however, I've noticed that the common measures of inflation are often based on food prices, and I suspect that the measures of "food inflation" will be somehow influenced by some other measure of inflation, so I've reached the point where I believe that I will need the help of the more skilled folks here. Is there an easy answer to this question?
The short answer is: No, the changes of food prices in the UK sometimes beat inflation, but not always.

To answer the question, you can simply look at the long term development of food prices in real terms. Note that "real" in the economic context generally refers to something being adjusted for inflation.

The graphic below, shows this development. It was taken from the Department
for Environment Food &amp; Rural Affairs. You can access the underlying data here: 



Now, why is it so often informally and apparently wrongly claimed that the price of food always goes up? I cannot provide you with a definitive answer, but I would assume that it is connected to the negativiety bias and the fact that most people generally tend to forget about inflation. Why do they forget? Well, maybe the italian economic-historian Carlo Cipolla was actually right.

Lastly: Does the fact that food prices have indeed risen in real terms in the UK, during certain periods, mean that human progress has indeed been going backwards, for a while?
No, not necessarily. We need to be aware that not only the price of the food we consume changes, but also its quality. For example: Regulations on food retailers, that grow evermore tightly, could lead to a continous increase in food prices but also reduce the number of foodborne illnesses. Human prosperity could therefore be growing, even while food prices increase.
This also means, that in some cases, it might indeed be rational to bet on an increase of food prices in real terms. Just dont stockpile food, the warehouse costs will almost certainly outweigh the gains and most food doesnt tend to get better as it ages.