Other cars being targeted by thieves include European popular models such as the Ford's Galaxy, Audi's A3, Toyota's Rav4, Volkswagen's Golf GTD and Nissan's Leaf.
Mr Beacham said Jaguar and Range Rover were constantly updating their technology in a bid to stay ahead of the scammers.
"Fortunately, New Zealand is too small a country for these kinds of criminals to operate in very easily," he said.
"The stolen cars would have to be shipped out of the country because it would be difficult to sell them on here."
Toyota and BMW had yet to come across the amplifier attack scam in New Zealand.
But Toyota NZ spokesman Morgan Dilks said car owners would find it difficult to guard against other than taking a few basic precautions with their vehicles.
"Owners should always know where their keys are, make sure their vehicle is always locked when unattended and is parked in a safe place," he said.
BMW New Zealand's corporate communications manager Edward Finn stressed the safety and security of customers was paramount.
"Anyone who has any concerns about the security of their car should contact their nearest authorised BMW dealer," he added.