Even for those who do not share the Brexiteers’ lust for life unshackled from Europe, there is, as with any divorce, something enticing; a frisson of illicit excitement in the prospect of once again being single.

Reasons for the breakup are many, but the common agricultural policy must be near the top of the list. For 40 years Britain has been subject to its perversities, inefficiencies and unintended consequences, creating bafflement, distrust and a generally dysfunctional relationship between farmers and the public. If there is a prize to be garnered from Brexit, it is in resetting this relationship, so fundamental to the health and wellbeing of people and planet.

In their mutual myopia, the National Farmers' Union and environmental zealots give the public a fallacious choice

Within the farming industry, there has been no shortage of talk about the historic opportunity to reshape the future. Michael Gove may bring enthusiasm to the task and greater political clout in cabinet than his department has enjoyed for decades, but if he is to succeed where his predecessors failed, he is going to have to turn his words into actions and actually make something happen. The 25-year environment plan, launched earlier this year, certainly provides an admirably bold ambition “to leave the environment for the next generation in a better state than we found it”.

Achieving this is a challenge in itself, but doing so while feeding a burgeoning population is an order of magnitude greater in complexity and ambition. To leave this challenge to the Department for the Environment, Food and Rural Affairs alone is to reduce it merely to an issue of agricultural practice and production, as has been the case for the past 40 years, in which time agricultural policy has become a flatulence-inducing stew of compromise, bad planning and incoherent bureaucracy.

The truth is that we all have a vested interest in how we balance the need for food with the needs of our natural world. There has long been a tiresome parrying of points between the National Farmers’ Union – purporting to speak for all of farming – and the environmental zealots purporting to speak for all things “natural”. Both sides have won the odd battle, but neither has won the war. The NFU’s catatonic insistence that the environment must be restricted to both the metaphorical fringes of UK agricultural policy, and the literal fringes of its members’ farmland, has failed to arrest a decline in much of our environment’s natural assets. It also obligingly sets up the environmentalists’ counter-argument that all of farming is presiding over nothing less than an ecological race to the bottom.

‘The public also has some changes to make.’ Sheep farming on Exmoor. Photograph: Tim Graham/Getty Images

While indulging in their mutual myopia, they give the general public a fallacious choice: either feed the people or save the planet. Neither speak for the many farmers, growers and environmentalists who hold a more considered and constructive view that farming and environment can, and must, work in beneficial and mutually sustaining symbiosis. For them, Brexit is an opportunity to restart the conversation.

The premise is simple: the purpose of farming is to deliver health; the health of our natural world and all the natural assets upon which life itself depends, and the health of our people, sustained by a balanced diet of wholesome, nutritious food. Defra’s consultation paper on the future for food, farming and the environment in a “green Brexit” links farming only to the health of our environment. It says precious little about the role of farming to produce nutritious food for a healthy population, and so does the government’s new plan to tackle childhood obesity. This at a time when the UK has surpassed the US as having the highest percentage of obese school-aged children, and obesity and poor diet have beaten smoking into second place for driving poor health in the UK.

The government must now do something it has never done before: enshrine into legislation the common mission to create and sustain a healthy population and natural world.

Even if some of us don’t yet know it, we really don’t want our farmers to stop producing food from the land they tend, but we – and they – may want to stop those ways of producing food that have the biggest impact on our environment, while making the least contribution to our health. Brexit will give Gove and his fellow ministers a generational opportunity, but on a matter so fundamental we must all participate in the public sphere, acknowledge the need to change our behaviours, and act. Farming has to speak less to itself and more widely with society.

When faced with bare facts such as declining soil fertility, farming’s contribution to the public discourse can no longer be limited to a staunch defence of the status quo. The public also has some changes to make: food waste, and profligate consumption of food, water and energy, drive demand for the most intensive and extractive methods of production. And no foodstuff, whether derived from animal or plant, is free of environmental cost or moral hazard.

The government’s next iteration of its policy on agriculture and environment is as central to all our lives as its policy and spending plans for education and health. An honest, balanced and trusted discourse between farming and society is much needed, but can only be established when we are all prepared to acknowledge our complicity in creating the problem, as well as our responsibility and ability to find a better way to sustain healthy people and planet.

• Catherine Broomfield writes on farming and keeps cattle on her grassland farm in Devon