It includes diesel-powered cars with the VW brand, Audi, Seat and Skoda as well as VW commercial vehicles.
In the next few days the company will give thevehicle identification numbers to retailers as well as coming up with a process for owners to check if their vehicles are affected.
VW will then start contacting owners.
The company stressed that all the vehicles are still safe and roadworthy.
VW plans to present its plans for resolving the problems with the affected vehicles to regulators next month.
The specific number of vehicles affected under each brand are:
Volkswagen cars 508,276
VW commercial vehicles 79,838
The UK was always likely to have substantial numbers of the diesel cars involved in this scandal.
And around half of all new cars bought here are diesels.
In 2001 Labour introduced a graded system for vehicle excise duty which penalised vehicles that emitted higher levels of carbon dioxide (CO2).
Diesels typically emit less CO2 than equivalent petrol cars. So many consumers have switched to diesel from petrol believing they could save money and go green.
There’s probably another factor too.
British consumers like quality brands and are prepared to pay for them. More than 900,000 of the almost 1.2m vehicles involved in the UK are VW and Audi branded models.
The emissions scandal began in the US when regulators discovered that certain vehicles made by Volkswagen were fitted with software that would make theirdiesel engines operate differently when they sensed that the car was being tested.
It meant that the vehicles emitted considerably more pollutants in real world driving conditions than they had in testing.
As a result of the scandal, VW chief executive Martin Winterkorn resigned and was replaced by former Porsche boss Matthias Mueller.
The carmaker has so far set aside €6.5bn to cover the costs of the scandal.
It has said that 11 million vehicles worldwide are affected, of which 500,000 were in the US
Also on Wednesday, the company has been giving details of the number of vehicles affected in other countries.
In France 984,064 vehicles were affected.
In the Czech Republic, where the Skoda brand began, Transport Minister Dan Tok said 148,000 vehicles were involved, of which 101,000 were Skodas.
The VW distributor in Portugal, Siva, said it had sold 94,400 vehicles with the roguesoftware.
It means the UK is the second most-affected country so far, behind Germany where 2.8 million vehicles will have to be recalled.
The company is facing legal action around the world.
On Tuesday the UK law firm Leigh Day wrote to VW saying it had “been approached by hundreds of people who own vehicles manufactured by Volkswagen and its subsidiaries”.
The letter encouraged VW to enter into negotiations about suitable compensation for owners as soon as possible.