Ministers have been accused of having to be “dragged screaming” to tackle illegal levels of air pollution across the UK, which kills an estimated 40,000 people a year prematurely.

Neil Parish, co-chair of a parliamentary inquiry into air quality, told ministers from the Treasury, environment, transport and local government departments they were showing no confidence that they would tackle toxic air pollution as soon as possible.

“We are not getting any clear message here about what you are doing about it,” he said. “The government is being dragged all the time screaming to put poor air quality right.”

A new air quality plan to reduce nitrogen dioxide emissions from traffic and other sources was produced this summer by the government. Previous attempts to cut air pollution were found to be so poor as to be illegal by the high court, and the government has been ordered to bring levels of nitrogen dioxide pollution within legal EU levels as soon as possible.

Five cities and 23 local authorities have been selected in the new plan to come up with measures to reduce illegal levels of nitrogen dioxide by December 2018. But the government refused to legislate for more “clean air zones” that would charge the dirtiest vehicles to enter the UK’s most polluted cities and has stopped short of bringing in a diesel scrappage scheme.

Minister were accused by MPs on the inquiry of passing the buck under the new plan to local authorities to make politically unpopular decisions about charging diesel vehicles.

Thérèse Coffey, environment minister, denied this. She said she was working with the local authorities to support them in drawing up plans. She said all but one of the five most polluted cities outside London – Southampton, Derby, Leeds, Birmingham and Nottingham – were on target to produce their draft plans in March next year and final plans in December 2018 for implementation in 2021. Derby, however, has yet to produce its preferred measures and she said she had concerns about whether they would keep to the timetable.

“Air quality is improving,” she said. “Not as quickly as we would like and we fully recognise we are in breach of one element of the air quality directive. We are actively improving air quality and I don’t agree we are being dragged to try and improve air quality … We have great urgency which has led us to direct councils to work on their plans.”

Coffey said she has written to all the 28 local authorities identified in the new air quality plan and government was providing help and funding through a £225m implementation fund and £222m clean air fund, which was announced in last week’s budget.

Coffey said councils were anxious about the prospect of charging drivers of diesel vehicles to enter their towns and cities. “We have to get these plans in place to achieve better air quality as quickly as possible, but if charging [drivers] is the only way they can achieve that then we will work with them [local authorities] on that. But I strongly believe most councils are desperate to try and find other ways to improve air quality.”

A Derby city council spokesperson said the council “takes the issue of air quality very seriously and we already have a number of measures in place to tackle it. We are currently undertaking work to develop additional measures to reduce air pollution that work best for the city of Derby.”

The inquiry into air quality has heard evidence from leading health professionals who described air pollution in the UK as a public health crisis. A report by the Royal College of Physicians and of Paediatrics and Child Health said last year that outdoor air pollution is contributing to an estimated 40,000 premature deaths a year.

Prof Stephen Holgate, asthma expert at Southampton University and chairman of the reporting group, told MPs on the inquiry that there were no safe levels of pollution from nitrogen dioxide.

The inquiry challenged ministers on their commitment to encouraging more people to walk, cycle or take public transport.

MPs said £46bn had been spent on funding tax breaks on diesel vehicles but just a small fraction of that amount – millions rather than billions – on air quality initiatives and green public transport.

Andrew Jones, Treasury minister, said the government had allocated £3.5bn over 10 years for air quality and cleaner transport initiatives, which he described as a “significant amount of money.”

The government’s new air quality plan was published in July, with a promise to ban petrol and diesel cars in 23 years. But leaders of eight of the most polluted cities have written to the environment secretary, Michael Gove, to say it is inadequate. They have called for called for urgent legislation and a proper diesel scrappage scheme, saying the air quality plan would not enable them to keep to their legal limits on pollution.