To me, far more likely is that locally grown food would be displaced by food grown in lower cost countries. That already happens to quite a degree in the UK, b

To me, far more likely is that locally grown food would be displaced by food grown in lower cost countries. That already happens to quite a degree in the UK, but it's mainly to make things available "out of season" from what I've seen. A significant hike in UK grown food costs, would just lead to more being imported, unless of course you start going down the line of more import tariffs which is of course possible but tends to have other consequences in terms of things like trade wars and reciprocal tariffs on UK produced goods. Of course you could eschew tariff protection and allow food production to move to other countries, but that in itself has potentially serious consequences as a trade war or some kind of event which disrupts supply from those other countries could endanger the food security of your country...