Some councils have had to rip up thousands of parking tickets, with one local authority – Brighton & Hove Council – being owed more than £750,000.
In South Yorkshire, Doncaster Council had to scrap up to £12,000 worth of tickets because of the problem.
The LGA said the EU allows European vehicles to be driven on UK roads for six months before the owner have to register with the Driver and Vehicle Licensing Agency (DVLA).
However, the Government does not keep a record of the estimated three million European vehicles entering the country each year.
The LGA added that the DVLA records information about non-UK-registered vehicles only when they are notified through offence reports provided by the police or from tip-offs from the public.
This means that foreign vehicles are able to disappear within the system by remaining unregistered.
The LGA added that this left town hall parking bosses facing an impossible task to chase down drivers for payments. But laws in other countries mean British motorists parking illegally abroad can be tracked and chased for payments.
LGA economy and transport board chairman Peter Box, who is also leader of Wakefield Council and chairman of the West Yorkshire Combined Authority, said: “Drivers of foreign-registered vehicles need to realise they are not above the law in this country.
“Reckless and inconsiderate parking by non-UK registered vehicles puts other drivers and pedestrians at risk.
“The millions of pounds worth of fines written off could also be spent filling potholes, providing bus services and tackling the £12bn repair backlog to bring our roads up to scratch.”
He added that “introducing a central database would allow the Government to get tougher on people failing to register their vehicle”.
The LGA said Oxfordshire, Southampton and Portsmouth councils have collectively been forced to rip up more than 10,000 tickets – £500,000 of fines – issued in the past five years to foreign-registered vehicles.
It said two per cent of all parking tickets issued in Brighton and Hove were given to vehicles registered outside the UK, at a value of around £2,000 a month. Brighton & Hove Council is owed more than £750,000 in unpaid fines.
In the past 12 months Bournemouth Council has been forced to write off £57,000 worth of parking fines to foreign-registered vehicles, while Maidstone Council in Kent has written off £28,455 worth of tickets.
Leicester City Council has written off £20,000 in tickets in the past year. And Torbay Council in Devon is owed £15,810.