"It's a bit ridiculous. The cop stuck his head in the window and asked us if this was an Uber and then told us to get out because Uber was operating illegally," said Thompson.
"We contacted Uber afterwards and they filed a police complaint on our behalf, so that's pretty cool."
Uber claims an officer has been targeting drivers and leaving passengers stranded. "We have filed complaints with the Independent Police Conduct Authority for this unacceptable and potentially dangerous behaviour," said Uber spokeswoman Katie Curran.
Police denied that claim, saying officers dropped off passengers at their homes or in the central city where licensed cabs were available - but confirmed "several private hire drivers" had been issued infringement notices.
"We take our responsibility to ensure public safety seriously and where police stop a vehicle that has passengers on board, police will look to ensure they have a safe way of getting home," said Inspector Jim Wilson, acting district commander for Auckland City Police.
The clampdown comes amid growing controversy over the service, which is increasing in popularity because of its easy access and low prices but is under fire from established taxi companies.
The Uber app works by connecting passengers with drivers in their city through their smartphone. Once a driver is available, a screen comes up calculating the fare.
Uber is registered as a private hire company, much like a limousine service, so must agree to a set fare and not use a meter.
That law has landed two drivers in court for allegedly using their smartphones as taxi meters.
Aby Philips and Ajay Singh Panai appeared in Auckland District Court last month facing two charges under the Land Transport Act. They were charged with determining a fare other than by way of a set fare or an hourly rate agreed with passengers at the time of booking, and with using a taxi meter to determine a fare.
They will reappear in court next month and could face fines of up to $10,000 if found guilty.
Uber launched in San Francisco in 2009 and now operates in 53 countries and more than 70 cities including Auckland and Wellington.
In several North American cities Uber has been accused of running an illegal taxi operation that flouts industry regulations.
Kate Styles, national manager operations for the Transport Agency, said it had met Uber to discuss the way it charged passengers.
"Uber has been clearly advised of its obligation [which is] to provide passengers with a set fare at the time of booking or an hourly rate," she said.