Diesel vehicles will disappear from roads much faster than expected, according to the European Union’s industry commissioner.

Elżbieta Bieńkowska spoke after the European parliament backed tougher rules to prevent manufacturers selling cars that produce far more toxic pollution when driven than in official tests.

The “dieselgate” scandal began when Volkswagen was caught cheating emissions tests in the US but it is now clear that almost all cars emit far more nitrogen dioxide than regulators intended. The scandal highlighted the EU’s lax vehicle regulations and on Tuesday the European parliament voted strongly in favour of a bill that would bolster EU oversight and allow Brussels to fine carmakers up to €30,000 (£26,000) per vehicle.

The new measures will eventually take diesel cars off the roads, Bienkowska said: “Diesel will not disappear from one day to another. But I am quite sure they will disappear much faster than we can imagine.” The mayors of Paris, Madrid and Athens have already signalled a future ban on diesel vehicles.

Also on Tuesday, the mayor of London announced tough new proposals to charge polluting vehicles for entering the UK’s capital and the national government may announce similar measures across the country in the coming weeks. “Frankly, we don’t trust the manufacturers,” Sadiq Khan said.

Under the EU measures backed on Tuesday, carmakers would no longer directly pay testing agencies for pollution measurements in a bid to break their cosy relationships. EU nations now have to fund car exhaust testing centres, although they may levy fees from car makers to do so.

Brussels would also get powers to carry out vehicle spot-checks and levy fines, while national authorities would be able to peer-review each other’s decisions. The law still needs to be finalised in negotiations between EU lawmakers, the European commission and member states.

However, the new measures stopped short of creating an independent EU-wide surveillance agency to monitor vehicle emissions, which was one of the key recommendations of a parliamentary report into the dieselgate scandal. National agencies were seen as too vulnerable to lobbying by powerful motor companies in the same country and the report accused EU legislators and governments of caving in to lobbying from the motor industry.

Keith Taylor, Green party MEP for the south-east of England and a member of the European parliament’s environment and transport committees, said: “UK Conservative MEPs were the biggest opponents of the dieselgate report and were responsible for watering down its findings, which excoriate their friends in the car industry.”

Julia Poliscanova, at the NGO Transport & Environment, said: “It is disappointing that MEPs have rejected the opportunity to make dieselgate history by establishing an independent agency. Nevertheless the parliament has strengthened the new powers for the European commission to spot check cars on the road and properly scrutinise national regulators. Overall this is a good package in response to the dieselgate scandal that has poisoned the air we all breathe.”

Corporate Europe Observatory’s campaigner Fabian Hübner said: “The car industry should never have had such a big leverage over emissions regulation. It’s a scandal for how long it has been the puppet master of commission and member states.”