Prof Paul Cosford, from PHE, said the report was the “distillation of best evidence” on tackling air pollution that local councils could implement.
He said cars going nowhere with the engine on “annoy me – I just think why are you sitting there with your car idling?”
“No-idling zones raise awareness in all our minds that ‘Come on, we don’t need to be polluting,’ he said. “It’s totemic.”
The report says the zones should be introduced outside schools, hospitals and care homes – to protect those most vulnerable from the fumes.
London’s Westminster Council already has marshals handing out £80 fines to car idlers.
Other recommendations include:
clean air zones with charges for polluting cars
promoting smooth driving by removing speed bumps and setting more 20mph (32km/h) speed limits
promoting electric cars, with more charging points in public places
training bus drivers in fuel-efficient driving
making it easy for people to walk and cycle
changing town planning to prevent homes and schools being in areas of high pollution
The UK has struggled to keep within EU limits on pollutants such as nitrogen dioxide (NO2) – with 37 of the 43 regions of the UK in breach of NO2 limits.
But the report says policies should be aiming to go much further than meeting legal limits.
Prof Cosford told BBC News: “The best estimate is 29,000 deaths in the UK [from air pollution], then why would we only want to reduce that to the legal amount?
“We want to reduce that to as close to zero as we can.
“We have developed clean water, and clean air is a basic issue of human health.”
The report from health officials comes as the UK government is about to be taken to court again over its plans for tackling air pollution.
Its draft plan has been dismissed as “toothless” and “weak” by critics.
James Thornton, the chief executive of ClientEarth, said: “It’s hugely significant that public health experts are raising the prospect of clean air zones, which could charge the dirtiest vehicles to enter the most polluted areas of our towns and cities.
“The government’s own evidence shows this is the most effective way to bring down illegal and harmful levels of air pollution as soon as possible, which ministers are legally bound to do.
“So it’s astounding that the government did not make this clear to people when it consulted on its air quality plans for the UK, forcing us to go back to the High Court next Wednesday to try to get them to do this.
“If this is going to happen, then people need to have their say on it.”
Dr Penny Woods, chief executive of the British Lung Foundation, said: “Air pollution is poisonous.
“We welcome the recommendations to introduce no-vehicle- idling areas, [and] clean air zones in the most polluted towns and cities will be vital in reducing toxic emissions and protecting us all.”