Farmers don't work in partnership between countries. They are bitter competitors. They barely work together locally, they are all fighting for the same piece of pie. Nothing has changed.Unfortunately, this answer, along with LT's answer earlier misses some rather important facts.
The huge agri-conglomerate EU is now a competitor, whereby it was a Partner.
Once we start factoring in subsidies to a free market economy, we'll never be able to stop. The Farmers will never be able to make their farms profitable as the cost of their products will be kept artificially low.
And the comparison to New Zealand is unfortunate. Before they went free market, they were in a Government backed, guaranteed price system whereby the Taxpayer effectively subsidised food production by allowing the Government to purchase all produce at a minimum price. Even if that minimum price was substantially higher (and it routinely was) than the market price. When they eventually dropped this policy, they were fortunate enough to have the worlds 2nd largest economy, coupled with the largest population effectively on their doorstep. China took everything they grew at a fair market price, allowing the NZ farms to invest in methods and machinery. We most certainly do not have this luxury. We'd be attempting to sell our produce into an already serviced market. We could only do this by reducing the price further, requiring more government subsidies. An ever spiralling debt cycle.
One of the benefits of withdrawing is that UK farming subsidy will no longer go to an olive farmer on Italy. It can be targeted at areas of UK farming that need it, justifiably hopefully, or where it benefits part of the UK for farming and beyond. The money should be better spent.