A scrappage scheme paying to remove the dirtiest diesel cars from the roads is unlikely to have a significant impact on air pollution, analysis suggests.

A study by the RAC Foundation found that around 1.9 million diesel cars fall into the oldest and most polluting categories, accounting for 17% of all diesel cars on the roads.

They are responsible for around 15% of the emissions of nitrogen oxides (NOx), pollutants linked to respiratory and heart diseases and premature death, from the diesel car fleet, the RAC Foundation said.

An estimated 40,000 people die early each year in the UK because of air pollution, with emissions from transport - particularly diesel vehicles - a major factor.

If a programme similar to the scrappage scheme introduced in 2009/10 as an economic stimulus for the car industry was run targeting diesel cars, it could take 400,000 of the oldest cars off the road.

It would cost some £800 million, with the Government and manufacturers both contributing £1,000 each to people trading their existing vehicle for a new model.

But the analysis suggests that even if all the 400,000 older cars were replaced by clean electric cars, the cut in pollution from the diesel fleet would be about 3.2% of all the emissions from diesel cars.

If scrapped cars were replaced by the newest diesel models which meet so-called "Euro 6" emissions standards, and were driven the same amount as the cars they replaced, it would cut NOx emissions by just 2,000 tonnes a year, or 1.3% of the total from diesel cars.

And if the new Euro 6 vehicles were driven as much as other Euro 6 vehicles already being sold - with all other vehicle mileage remaining the same - it could actually push emissions up slightly, the analysis said.

It would also be hard to ensure that the scrappage scheme focused on cars being used in big cities where air pollution is of greatest concern, the RAC Foundation said.

Rather than focusing on a diesel scrappage scheme, the RAC Foundation urged the Government to look at spending the money on different areas, such as increasing charging points for electric vehicles and ensuring they continue to have subsidies.

Air pollution from heavy duty vehicles such as lorries, buses and taxis also needs to be tackled.

Steve Gooding, director of the RAC Foundation, said: "Instinctively a scrappage scheme to get the oldest, dirtiest diesels off the road seems like a good idea. But these numbers suggest otherwise.

"At best it looks like emissions would be reduced by only a few percent, unless government was prepared to launch a scheme on an unprecedented scale.

"The big considerations for any scheme include: where diesels are being driven, how far they are being driven and how do these factors change with the age of the vehicle.

"Before being tempted to go down the scrappage route ministers need to ask if the sums might be better spent elsewhere, for example in making sure that the infrastructure is in place to support plug-in electric vehicles."