An ultra low emission zone in London for the most polluting cars will come into force in April 2019 and reports say other cities will follow suit.
The government will also produce a new air quality plan by the end of April.
But Theresa May has said she will "take into account" drivers encouraged to buy diesel cars by previous governments.
Former Labour Chancellor Gordon Brown introduced a lower vehicle tax in 2001 to encourage people to buy diesel cars, as they were more economical and thought to be less harmful in terms of carbon dioxide emissions.
But there has been increasing concern from experts that the vehicles emit dangerous levels of nitrogen dioxide, which is thought to have caused thousands of premature deaths in the UK.
The government has to produce a new air quality plan after receiving a "final warning" from the European Commission about breaches of legal air quality levels in the UK.
It also lost two court cases in 2015 and 2016 over pollution levels brought by environmental lawyers ClientEarth.
To tackle the issue, a so-called "toxin tax" is expected to be rolled out across several cities, charging drivers of diesel cars up to Â£20 per day to come into urban areas.
Mayor of London Sadiq Khan announced on Tuesday that such a scheme - creating an the ultra low emission zone in the capital - would come into force in two years' time, with a charge of Â£12.50 for petrol cars that do not meet Euro 4 standards and diesel vehicles that do not meet Euro 6 standards.
But motoring organisations have said diesel car drivers are being "punished" for following a previous government's policy.
Mrs May has now hinted there will be schemes to help drivers who were told that diesel vehicles were the right purchase.
Speaking on her trip to Jordan and Saudi Arabia, she said: "Decisions will be taken when we produce that [air quality] plan.
"But I'm very conscious of the fact that past governments have encouraged people to buy diesel cars and we need to take that into account when we look at what we do in the future. "
She did not set out any specific plans, but there have been reports of a scrappage scheme that could pay people to get rid of their diesel vehicles.

Griffin Place Communications Limited, in Llantarnam, Cwmbran, employed up to 140 people, with many staff claiming they were sacked days before.
Torfaen AM Lynne Neagle said the Welsh government has "serious questions to answer", while Welsh government said it would be reviewing the situation.
Attempts have been made to contact the company for comment.
On Friday, employees arrived at the Llantarnam offices to find the rooms empty and the doors locked.
The company has notified some workers that it has commenced liquidation proceedings and many of those have claimed they are owed thousands of pounds in wages.
A letter to employees from insolvency firm Finn Associates advised there will be a meeting of creditors on 13 August.
Ms Neagle has arranged a public meeting for former workers on Monday at Mount Pleasant Hall in Pontnewydd.
"The immediate priority now has got to be to try and support the many staff who have been devastated by this news," she said.
Shadow Economy Minister William Graham said Welsh taxpayers "will rightly question" whether Welsh government's investment in the project represented value for money.
Torfaen council confirmed it will be contacting seven clients employed by the company as part of the UK government's Work Programme.
According to the Welsh government, support provided to the company stipulated jobs should be in place for at least three years.
"We will, with immediate effect, be seeking repayment of relevant grant sums," the spokesperson added.
"We have also mobilised the Welsh Contact Centre Forum, who can signpost affected staff to potential new job opportunities, and we will keep the situation under review."

Ed Joyce and Chris Nash both hit half-centuries between interruptions in play, before Nash was bowled by Rob Keogh for 53 before lunch.
Joyce was trapped lbw by Ben Sanderson after the break to give the visitors a slight hope of grasping a win.
Bad light stopped play with the hosts 145-2 as they held on to share the points with no further play possible.
Northants' seventh draw from their eight Division Two matches leaves them seventh and leave them trailing leaders Essex by 34 points.
With only one side promoted from the second tier this season, both sides are struggling, with Sussex lying in sixth position and only three points better off - albeit with a game in hand.
Diesel car owners could get some help from the government if cities adopt new charges to tackle pollution, the prime minister has suggested.
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A call centre in Torfaen which received £600,000 funding from the Welsh government has gone into liquidation.
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Heavy rain denied Northants the opportunity to push for victory as they drew against Sussex at Arundel.