Minimum wage remains minimum wage, and local produce remains local produce with local margins. The numbers only change if the produce is for export (mostly not) or if workers are hired from abroad because locals won't do the work (possible, but increasingly expensive.)

Just because import tariffs make foreign food more expensive doesn't mean the local economy grows automatically to take up the slack. There's still the possibility of a dead zone in which affordable local prices don't cover costs even as foreign prices become completely unaffordable.

This has the makings of a complete market failure. Combine an impoverished population which can't afford to pay a realistic price for food, with farmers who can't afford to stay in business without subsidies (nonexistent) or cheap labour (also nonexistent), and the most likely outcome is bankrupt farmers and food shortages.

The worst case is an authoritarian dictatorship which forces people to work on farms at gun point. Worryingly, this may be the only practical way to solve the problem - short of an even more extreme measure, such as cancelling Brexit.