Owen Paterson is exactly correct here

One of the things that Brexit allows us to do is the sensible thing which EU membership stops us from doing. Kill off entirely the subsidies to the agricultural sector:

Farmers reacted with fury last night to a proposal to axe their £3 billion in taxpayer handouts after the UK leaves the EU.

Former Environment Secretary Owen Paterson told a secret ‘Brexit seminar’ of former Cabinet Ministers at an Oxford college that Theresa May should follow the example of New Zealand, which ended government help for farmers virtually overnight in the 1980s.

The shock forced a radical shake-up in the country, with sheep farms replaced by deer parks and vineyards.

Well, yes, they would react in fury of course but it's still the sensible thing to do. As we've noted before the current subsidies don't in fact achieve much anyway, other than a rise in hte price of land:

We have an alternative policy framework to suggest. Let's just not have a policy. No subsidies, no payments, no department, no Minister, nothing, nowt, zippedy dooh dah. The New Zealand option. You've had it good for a century or more now there's yer bike and have a nice ride.

For that major support is these days the flat payment per acre being farmed. And as David Ricardo pointed out, that's just an addition to the rental value - and thus increases the capital value of the land. The current system of subsidy thus just raises land prices, meaning that people who want to go into farming must pay more to do so - it doesn't increase incomes over the long term at all.

Kill the entire system stone dead.