Marvin Rees has been told in no uncertain terms that the people of Bristol must have cleaner air.

In a sternly-worded letter, one of the most senior ministers at the Department for Environment, Food & Rural Affairs (DEFRA) warned that Bristol City Council could face legal action if there is any further delay to deadlines that have twice been missed.

A consultation on transport proposals to reduce air pollution in the city closes on Monday.

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Writing to Rees, parliamentary under-secretary of state Thérèse Coffey said: “You have been provided with all the necessary support and funding for you to develop a proposal to submit to Government to deliver NO2 compliance in the shortest possible time.

“For the avoidance of doubt, I want to be very clear that your preferred option must deliver compliance in your local area in the shortest possible time, and have a robust evidence base to support it.”

Coffey stressed that clean air zone compliance should be achieved in Bristol by 2025 at the latest, following implementation of the required measures in 2020.

Within the current consultation, these is either a clean air zone in which private cars are not charged or a diesel car ban which would prevent all diesel cars from driving in a specific central area from 7am to 3pm.

Coffey said: “I want to be clear that any further delay to your project, which risks a delay to the delivery of compliance is unacceptable.

“I would like to make clear that any delay or non-compliance with the September and December deadlines will result in me being forced to consider legal action against Bristol City Council which may include issuing proceedings without further notice.”

She added: “It is vital that you work with my officials… so they can provide support and assistance. I do not believe the level of engagement with the team has been to an acceptable standard to this point.

“I am very concerned that, without engaging fully with the team, you will be further delayed in delivering on your plans and therefore ensuring the people of Bristol have access to cleaner air.”

Rees said that he has already “been clear that Bristol is committed to improving air quality in the shortest time possible, and this remains both our intention and what we are legally required to do”.

He said: “The government’s direction is telling us to do things that we are already doing or planning to do, to the timescale that we had already set out. We are in close contact with them about the detail following our announcement two weeks ago that we were looking again at available options and doing the technical modelling work required.

“A Clean Air Zone type D – which includes charging private cars as part of congestion charging – is not one of the options that we are consulting the public about. This is because previous modelling work had not indicated that it would help us achieve better air quality sooner than the options we have presented.

“As part of due diligence it is right that this is looked at again, this time adding in the various additional measures proposed in our existing preferred options to see if anything changes. Again, this is work that our consultants had already been instructed to do.”

He added: “We are very conscious of the potential impact of charging private cars. We have particular concerns about the impact on some of Bristol’s poorest people, but also on many other hard-working people who have been pushed even closer to the edge by years of austerity and disinvestment in public services by the government. Any CAZ option which could be taken forward will have technical modelling done to test the social and economic impacts.

“We continue to work with officers from the government’s Joint Air Quality Unit frequently and do not recognise the minister’s critique of our level of engagement, particularly given we last wrote to her with an update in March and did not receive this reply until late July. We will continue to engage frequently – and in good faith – with the minister and JAQU.

“Of course this whole process is part of a much wider collection of actions we are taking to tackle the issue of air quality. Alongside it we are negotiating a new bus deal for the city, we’re looking at closing roads around schools during drop-off and pick-up times, and we are transforming the city’s relationship with energy through our City Leap project, a series of energy and infrastructure investment opportunities. But as much as we’re doing, we need to be empowered and funded to do more.

“We continue to press government for the investment, legislation and focus we need to make it easier rather than more difficult to deliver meaningful change, including the right investment in housing and transport infrastructure that will enable inclusive and clean economic growth.”

Read more: Polluting NO2 levels twice the legal limit in parts of Bristol