Nearly one in 10 diesel cars in the UK is fitted with the software that caused the Volkswagen emissions scandal.
The German car-maker said it would contact the owners to arrange for their vehicles to be "corrected".
VW confirmed that nearly 1.2 million UK vehicles are affected, consisting of 508,276 Volkswagen cars, 393,450 Audis, 131,569 Skodas, 79,838 VW commercial vehicles and 76,773 Seats.
The Wolfsburg-based company insisted its vehicles - which have EA 189 engines fitted from around 2009 to this year - are ''technically safe and roadworthy''.
VW has not confirmed how the modification will take place.
It will give the identification number of affected vehicles to retailers "in the coming days" and then customers will be contacted.
The firm will also set up a system for drivers to check for themselves if their vehicle needs modifying.
The scandal began in the US, where the Environmental Protection Agency said 482,000 Volkswagen vehicles were fitted with sophisticated defeat device software, which switches engines to a cleaner mode when they are undergoing official testing.
Once on the road the cars produced nitrogen oxide pollutants at up to 40 times the legal standard.
VW has admitted that 11 million of its diesel vehicles worldwide were fitted with the software.
The company said that just over 1.1 million UK cars are affected, which is 9.9% of the country's diesel cars. Latest figures show that 11.2 million are licensed for use on UK roads.
Transport Secretary Patrick McLoughlin told the company's bosses to resolve the issue quickly.
He said: "The Government's priority is to protect the public and I understand VW are contacting all UK customers affected.
"I have made clear to the managing director this needs to happen as soon as possible.
"The Government expects VW to set out quickly the next steps it will take to correct the problem and support owners of these vehicles already purchased in the UK."
VW has announced how many vehicles are affected in a number of other countries, including France (984,064), the Czech Republic (148,000) and Portugal (94,400).
The UK has the second largest number of vehicles so far, behind Germany which has 2.8 million.
Martin Winterkorn resigned as VW chief executive as a result of the scandal. He was replaced by former Porsche boss Matthias Mueller.
The firm's share price has fallen by 40% since the scandal broke on September 18.
A number of UK law firms claim they have been contacted by hundreds of motorists interested in a group action against VW.
London-based firm Leigh Day has written to Mr Mueller to call for compensation for those drivers who paid a premium for "clean" diesel cars.
Richard Lloyd, executive director of consumer group Which?, said: "We now need the Government to urgently set out a timetable for action so that consumers can get redress.
"We also want the rest of the car industry to swiftly set out whether their tests have been manipulated and if their customers have been misled."
The British Lung Foundation has called for proposed changes to European testing of vehicle emissions to be implemented as soon as possible.
The charity's chief executive, Dr Penny Woods, said: "It is clear there is a dire need for a commitment to routine, independent real-world testing on all cars.
"The Government is currently consulting on air quality plans - if our leaders wish to keep a clean conscience they must act now to help protect future generations from dirty, dangerous air."