Ford has announced it will discount £2,000 from some of its new models if the buyer agrees to scrap their old car.
The deal will apply to cars of any brand built before 2010, and will include petrol engine as well as diesel cars.
Incentives by rivals such as BMW and Mercedes have only included diesel cars, meaning this offer might be taken up by many more car owners.
All of the part-exchanged cars would be scrapped, according to the US car giant, which it said would have an immediate impact on air quality.
Environmental campaigners greeted the news positively but said the government needed to do more to tackle air pollution.
Ford will honour the part-exchange scheme until the end of December.
Andy Barratt, chairman and managing director of Ford of Britain, told the BBC's Today programme, "We have some pretty large incentives here, up to £7,000 if you have a commercial transit vehicle.
"We're the only scheme open to commercials. It is part of a journey.
"Air quality is a much bigger debate and getting older vehicles off the road is part of that.
"New technology, such as plug-in hybrids etc., are all part of that longer journey we need to work together."
The government has been working on a clean air strategy in recent months, but so far has not come up with any kind of scrappage scheme. However, a consultation on the subject is proposed for later in the year.
Crucially, however, the government did say that both petrol and diesel cars would be banned from 2040.
The announcement came following the defeat of the government in a case brought by environmental law campaigners ClientEarth over contraventions of EU emissions standards.
ClientEarth lawyer Anna Heslop praised Ford's move, but railed against government inaction on the subject.
She said: "At the moment, there are pockets of small, short-term actions here and there, but nothing like the joined-up thinking we need to solve this problem."