But Tory MPs will urge the Government to commit to a targeted scheme in the House of Commons debate on Wednesday next week.

Neil Parish, Conservative chairman of the environment, food and rural affairs select committee, will say: “I know there are concerns about the costs of any scheme.

“That’s why any proposed scheme should be targeted and proportionate. It should be a key weapon in the armoury of the Government in tackling air pollution problems.”

He will say the scheme could be limited to the 5.6million diesel cars which were registered before 2005 and "geographically" targeted in "pollution hot spots".

He will say: “Limiting the scheme to these hotspots could potentially take as many as half of these dirtiest diesels out of these pollution hotspots.”

Scrappage schemes have proved to be very popular, with seven in 10 AA members supporting the policy.

A previous scheme in 2009/10 allowed a vehicle to be scrapped for a £2,000 discount on a new car, with £1,000 from the manufacturer and £1,000 from the Government.

Mr Parish will propose that the new scheme follows the same rules but should be means-tested so that it does not become “a subsidy of the middle class”.

He will say: “Households should not just be able to trade in multiple diesels for a cash subsidy.