Stocks locally are currently fine, but if you think logically about where a large percentage of our food comes from, Brexit is inevitably going to have a knock-on effect on the food security we've previously taken for granted, often without thinking, or caring, about the knock-on effect on people in the countries supplying them. (Yes, quinoa, I'm looking at you.)
One of the main reasons we're in the mess we're currently in is that people panic and don't think logically, and vote based on (what they're told by the media about) personalities, not policies and actual evidence of the actions of those personalities.
Several university institutes have been looking at food security in general for years now. Throw in a bit of climate change and COVID-19 for good measure, not to mention the way humans generally behave, and I think it's amazing the supermarkets and other suppliers have done as well as they have.
Food is likely to get scarcer, less varied and more expensive, for a while at least, and our diets are likely to change. There'll be far less meat, and, given the way the government has decided to remove sustainability from the wording of the UK's "Give us wor fishing rights back or else" bill, it's likely fish will become even more of a luxury than it already is in the future too. If you're old enough to remember the 1970s, I suspect it'll be a lot like that crossed with the 1940s/1950s for a bit, only much less joyful. Still, I hear there's a new unicorn sanctuary on the Kent coast that's a great day out for a family. ;)