They also copy the genuine vehicle's log book - or V5 form - by using one of thousands of blank DVLA documents that went missing some time in 2006.
"We're recovering about ten a week and we think there's easily over 120 to 130,000 stolen blank documents out there still," DCI Mark Hooper from the Association of Chief Police Officers' (Acpo) vehicle crime intelligence service, told BBC 5 live's Donal MacIntyre programme.
"It will keep me very busy, and my team very busy, for the next hundred or so years, I suspect."
Hundreds of people have fallen victim to car cloning and the Acpo unit says it has recovered £13m worth of stolen, cloned vehicles in the past 18 months.
Shona Topping from St Albans was a cautious used-car buyer who had always driven company vehicles
Shona Topping had to surrender her car and lost the £8,000 she paid for it
When she spotted a Mercedes she liked in a magazine, she asked for its registration details so she could run a vehicle data check on its history.
"I took a mechanic along to have a look at the vehicle, carried out the check and obviously, being nervous, I had to do everything possible," she said.
"It tells you on all the advertising that they check various databases, checking with the police on the computers."
But because Shona's car had been cloned, she was actually running data checks on a completely different, legitimate car.
That meant the result came back clean.
Shona lost £8,000 because she paid for the car in cash.
"I actually hold the DVLA responsible because it's operated as a tool for the criminals," she said.
"They definitely would not have been able to carry out this crime without the help of a perfect, blank V5 form".
The DVLA has published on its website a list of serial numbers for the blank log books which it believes have gone missing.
Acpo's DCI Mark Hooper advises potential used-car buyers to check the documents' serial numbers against the missing batch.
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