Environmental groups have welcomed calls for the ban on new petrol and diesel cars to be brought forward.
Rosie Rogers, clean air campaigner at Greenpeace, called on the ban to be implemented by 2030 at the latest.
She said: "We now know diesel is toxic so there can be no more excuses and no more delays.
"The Government must prioritise public health and bring forward its phase-out date by at least 10 years.
"Other countries have managed it, and people who live in the UK deserve clean air just as much."
Simon Alcock, head of public affairs at environmental law firm ClientEarth - which has successfully challenged the Government's air quality plans in the courts, claimed the committees have produced a "landmark report".
He said requiring car manufacturers to contribute to a clean air fund is "a perfect response to help consumers who were misled into thinking their vehicles were cleaner than they actually are".
Martin Tett, environment spokesman at the Local Government Association, said: "The 2040 target set by the Government for the end of the sale of conventionally-fuelled vehicles is too far away to tackle a public health problem that is shortening lives now.
"It cannot overlook the immediate measures that could have drastic improvements on public health in areas where air quality problems are at their most severe."
Alison Cook, director of policy at the British Lung Foundation, said diesel is an "invisible danger" and "the sooner these vehicles are off our roads the healthier we will all be".
Nicholas Lyes, the RAC's head of roads policy, urged the Government to do more to encourage drivers to choose cleaner vehicles.
"Now is the time to ask whether incentives such as the plug-in grant scheme are doing enough to change drivers' buying habits," he said.
"The Government may need to be far more radical."