The National Farmers' Union has ambitions for the sector to reach net-zero greenhouse gas emissions by 2040, a decade ahead of the UK economy as a whole, and has published a report on how it thinks it can be done.
It aims to meet the target by reducing emissions from farming practices, increasing the ability of land to store more carbon, and by focusing on renewable energy and products that remove carbon from the atmosphere.
British farms are responsible for around a 10th of UK greenhouse gas emissions, but only 10 per cent of its output is carbon dioxide, while 40% per cent is nitrous oxide from things such as fertilisers, and 50 per cent is methane from cows and sheep.
Agricultural emissions have fallen by 16 per cent overall since 1990, but there has been only "modest progress" since 2011, the NFU report says.
Farm businesses can make an important contribution to the UK's legally binding target to cut its climate emissions to zero, and over the next 20 years work could reduce, offset and balance out the 45.6 million tonnes of emissions agriculture is responsible for, the NFU said.
Efforts to cut on-farm emissions could include improving health in cattle and sheep to reduce methane emissions, precision farming for crops to deliver nutrients and pesticides more efficiently, and reducing soil compaction to cut the need for cultivation and minimise nitrogen emissions.
Ways farms can store more carbon on the land include providing bigger hedgerows, more woodland and trees and boosting the carbon storage of soils, including peatland and wetland restoration.
Farmers can also contribute by supporting renewables, including energy from plant materials combined with technology to capture the emissions when it is burned for power.
Novel plant-based building and insulation materials such as hemp fibre and sheep's wool could also help lock up carbon from the atmosphere, the report said.
Much of the focus on cutting emissions from food production has been on reducing meat and dairy, but the NFU said the carbon footprint of British red meat was only 40% of world averages and it was important not to export the problem by shifting production to other countries.
NFU president Minette Batters said: "There is no doubt that climate change is one of the biggest challenges of our time and rising rapidly on the political agenda both at home and globally.
"Representing British farming, we recognise our unique position as both a source and a store for greenhouse gas emissions and, importantly, how we can build on our work so far to deliver climate-neutral farming in the next 20 years.
"We aspire to be producing the most climate-friendly food in the world.
"We must avoid anything that undermines UK food production and merely exports our greenhouse gas emissions to other parts of the world."
Ms Batters said work on her own Wiltshire beef, sheep and arable farm included improving grazing pasture with more clover and herbal mixes to fix nitrogen and use less fertiliser, and GPS technology was helping precision farming.
As the Government moves to replace the existing system of EU subsidies with payments that reward environmental "goods", the NFU is calling for support for improving productivity, enhancing hedgerows, planting trees, restoring peatland and backing for land-based renewables and new building materials.