The government will be more than a decade late in meeting EU targets on air quality, a report from the National Audit Office (NAO) has revealed.

The cost of health impacts from air pollution, including fine particulate matter and nitrogen oxides, is estimated at £20bn. Nearly 30,000 deaths were thought to be caused in 2008 by fine particulate matter pollution, some of it caused by diesel cars, according to the report. About 13% of fine particulate matter pollution is thought to come from diesel engines. This is in spite of improving air quality overall.

Emissions of nitrogen oxides and fine particulate matter fell by roughly 70% from 1970 to 2015, according to the report, released on Wednesday.

Moving away from coal-fired power stations to an increasing number of gas-fired power stations, as well as renewable electricity, was a leading cause in the reduction in pollutants, the report found. Road pollution is now the biggest cause of pollution from nitrogen oxides, but pollution from fine particulate matter comes from a diverse range of sources, including agriculture, according to the NAO.

The report from the NAO shows that air quality is a rising concern, but the government is not committing to publishing a review of the current legislation until next year.

Most of the UK’s current air quality requirements under the law come from the European Union. While the government has indicated that it would continue with current air quality standards after Brexit, it has consistently failed to meet current standards since 2010, and there is no indication of how the government would be held to account for future failures after leaving the EU. Currently, the government can be taken to court for its failures, but there is no such safeguard after Brexit.

James Thornton, chief executive of the environmental law pressure group ClientEarth, which has repeatedly taken the government to court over its failure to meet EU standards on air quality, said the report marked an important moment in the fight against widespread air pollution.

He said: “The NAO report lays bare the stark facts on air pollution affecting many areas of the UK, and illustrates why we have been forced to take the government to court for failing to produce a plan that would reduce the country’s illegal and harmful levels of air pollution to the shortest time possible.”

He added: “The government has passed the buck to local authorities and the NAO raises questions about whether it is doing enough to support them. Many more towns and cities have illegal levels of pollution than the 23 which ministers have pinpointed in their latest flawed air quality plan. We need much more action from the government and next week’s budget must contain measures which encourage a move away from diesel and on to cleaner forms of transport.”

A Defra spokesperson said: “Air pollution has improved significantly since 2010, but we recognise there is more to do which is why we have put in place a £3bn plan to improve air quality and reduce harmful emissions.

“We will also end the sale of conventional new diesel and petrol cars and vans by 2040, and next year we will publish a comprehensive clean air strategy which will set out further steps to tackle air pollution.

“We now have an opportunity to deliver a Green Brexit and improve environmental standards as we leave the EU.”