It is not far fetched to imagine a situation where a hard Brexit results in extreme languish of imported food and staple goods into the UK. Austerity was hard enough on the poor - Imagine if food prices doubled or tripled due to tariffs and currency devaluation. Not to mention the land border in Ireland returning to skirmish with patrols and violence.
This is one of the claims that keeps undermining the Remain position.
The EU imposes high tariffs on food in order to protect French farming. This is well known and has been discussed for years, often in the context of "when will Europe stop making Africa poor by refusing to buy its food".
A big part of the argument for leaving the EU is that British farming is a lot more efficient, so doesn't need so much protection, so food prices could be lower after exit. Why would the government raise tariffs on food so high its own population starved? That would make no sense at all.
What has Brexit got to do with that?