The government has set out new plans on air pollution that ministers say go beyond existing EU rules, with a pledge to improve air quality nationwide to the standards the World Health Organization (WH0) recommends.

Farmers will be subject to such air quality regulations for the first time to cut their growing contribution to pollution, under the government plans set out on Monday, while diesel vehicle drivers and owners of wood-burning stoves will also face restrictions.

Under the government’s plans, only the cleanest forms of biomass stoves will be available from 2022, and farmers will be required to reduce their fertiliser use and the emissions of ammonia – a potent air-polluting gas, which can combine with other forms of air pollution to lodge small particles deep in the lungs – from fertiliser and livestock. Sales of bituminous or traditional house coal may also be phased out.

Ministers said the number of people living in areas with pollution above WHO guidelines would be halved by 2025. The government said air pollution was one of the biggest threats to public health in the UK, behind only cancer, obesity and heart disease.

But critics said the plans were short on detail, with no deadlines for meeting the WHO limits, and fell short of the status of EU targets, which are enshrined in law. Legal challenges to the government over its failure to adhere to EU rules, which resulted in a supreme court ruling against ministers last year, have played a key part in bringing air pollution to government attention in the last five years.

The social and economic costs of air pollution in the UK were likely to be greater than previously thought, the government said, citing calculations that the cost of air pollution could reach £18.6bn between now and 2035. Ministers said the new plans should reduce the cost to the NHS and society by £1.7bn a year by 2020, rising to £5.3bn a year from 2030.

Fresh science on the dangers of air pollution has been piling up. On Saturday, the Guardian reported new evidence that air pollution can increase the risk of miscarriage in early pregnancy, compared by one doctor to the effects of smoking. In recent years, studies have linked air pollution to dementia, heart conditions and birth defects. About 7 million people a year are estimated to die from air pollution around the world.

Michael Gove, the environment secretary, said the UK needed a new strategy to improve air quality. “The evidence is clear: while air quality has improved significantly in recent years, air pollution continues to shorten lives, harm our children and reduce quality of life,” he said.

After Brexit, the UK will no longer be subject to EU legislation on air pollution, which the government has flouted repeatedly in the last decade, and which has formed the basis of challenges by campaigners that have forced ministers to change course and put in place measures to reduce the problem.

The government is aiming to phase out sales of new petrol and diesel cars by 2040. Photograph: Christopher Thomond/The Guardian

The government has not made it clear whether there will be new legislation that would allow ministers to be held to account in future over the commitments they are making.

Simon Alcock, the head of public affairs at ClientEarth, a legal advocacy group that has taken the government to court on several occasions, called for a clearer framework: “Action to protect people’s health must be a requirement, not a nice-to-have.”

Gove said traffic pollution – targeted by campaigners as the key source of small particles that lodge deep in the lungs, and nitrogen oxides and other gases that irritate the breathing passages – was only part of the problem. “While air pollution may conjure images of traffic jams and exhaust fumes, transport is only one part of the story, and the new strategy sets out the important role all of us can play in reducing emissions and cleaning up our air to protect our health,” said Gove.

There were no new major measures in the strategy to combat pollution from vehicles, but a restatement of last year’s pledge to end the sale of new conventional petrol and diesel vehicles by 2040, which campaigners said was too far away.

Morten Thaysen, a clean air campaigner for Greenpeace UK, said: “The government is saying all the right things about the huge cost in human lives and money, but is proposing nothing new to tackle pollution from road transport. A 2040 phase-out date for diesel and petrol is effectively saying that yes, your grandchildren deserve clean air, but your children will have to go on breathing toxic fumes so as not to disrupt the car industry’s sales forecasts.”

A spokeswoman for the Department for Environment, Food and Rural Affairs told the Guardian: “We will not weaken our environmental protection when we leave the EU, but will maintain and even enhance our already high environmental standards. Our clean air strategy shows how we will go further and faster than the EU in reducing human exposure to particulate-matter pollution. This will be underpinned by new England-wide powers to control major sources of air pollution, plus new local powers to take action in areas with an air pollution problem.”