It is believed cards are being skimmed at petrol stations, whereby the card details and pin numbers are retrieved and money withdrawn from the account.
About 200 of the UK's 9,500 petrol stations are thought to have been hit.
The Sri Lankan government has claimed its opponents, the Tamil Tigers, are behind the scam.
Police are investigating complaints made in Edinburgh, Norwich, Bury St Edmunds, Peterborough, Nottingham, Leeds, Bristol and Hull.
In Hull, the economic crime section of Humberside Police are checking thousands of receipts for fuel bought with credit or debit cards at one petrol station.
Detective Inspector Paul Welton, of Humberside Police, said "Quite clearly this was well-organised and it was done on an international basis."
Those alleged to have been involved were able to obtain card details and pin numbers and put them together to clone the cards, police said.
The site in Hull is now under new management, and the new owners are not linked to the police inquiry.
Sean Gillespie, one of thousands of possible victims, noticed his bank account was being emptied of small amounts over weeks, amounting to thousands of pounds.
"I knew how much had been taken but how it was taken was an absolute mystery to me," he told BBC News.
'Arms funding'
Most of the UK's petrol stations are independently run which means they are susceptible to being infiltrated by organised crime.
And the Sri Lankan Government believes it is the Tamil Tigers who are using threats to coerce innocent Sri Lankans to take part in the scam.
They say Tamil asylum seekers arriving in the UK are loaned money to open a petrol station, and once established they supply information to the Liberation Tigers of Tamil Eelam (LTTE).
Maxwell Keegel, first secretary of the Sri Lankan High Commission in London, said: "They extract the pin and details from the cards and within minutes this information is sent to LTTE agents who operate in remote parts of the world, as far away as Thailand and Indonesia.
"And the money goes unwittingly from people's accounts and ends up going into the LTTE's arms activities."
The petrol industry accepts it is a problem.
Some retailers have already replaced all their chip and pin machines, while some consumers are only using cash to buy petrol.
Nick Vandervell, of the UK Petroleum Industry Association, said "We are working with the independent retailers but it is difficult to tell them what to do."