There is very little we can be sure of about Brexit. A Free Trade arrangement of some sort accompanied by a deal on free movement would mean that it made very little practical difference for many of us; a straight-out departure falling out of and with the EU would be considerably more problematic.
However, for the agri-food sector and farmers in general, it is hard to see how the situation can be salvaged. The reason for this is CAP (and CFP); this is designed precisely as a protectionist policy for European agriculture and fishing. There is no precedent for any country outside the EU to have free access to the Single Market for agriculture precisely because of the purpose of EU policy – protectionism.
It is being suggested that, given the balance of agricultural trade, perhaps the UK could be the first exception and receive free access to the Single Market in this area. Leaving aside that the whole point of leaving the EU, according to the likely next UK Government, is doing trade deals (which would surely include agriculture), this is politically unrealistic. EU protectionism will see UK produce discriminated against within the remaining EU, and that will be that. This means, regardless of subsidies, UK farmers will simply have no one to export to (at least without tariffs being applied).
Why did no one tell them that before the referendum? They did. Leave-voting farmers will have brought this upon themselves.