Taking milk as a good example, if we decided to slap a 100% import duty on milk from the EU, to make its cost similar to what a UK non-subsidised farmer could produce it for, I can't imagine that they'd accept that without retalliating in some way.

The problem is that - in or out of the EU - they're still going to be our biggest trading partner.  I reckon it's going to be a complete mess for years, mainly due to the EU's absolute arrogance.  They actually have rules against state subsidy of industry, while at the same time paying farmers to give their produce away for next to nothing.