Hamish and Oscar Day have been charged with multiple offences including robbery, assaulting an officer, attempted bribery and driving a motorcycle without a licence.
Mestanza said local police were still sorting out exactly what happened, but there appeared to be an offer of a bribe, and the fight began when the officer took out his phone to take a photo of the licence plate.
He said the incident was part of a larger crackdown on foreigners in Thailand.
One case in Phuket - involving a Swiss ex-pat who kicked some Thai people who were sitting on the steps of his villa - has seen the Phuket governor and immigration police pledge to deal more strongly with people who were breaking Thai law.
“This is two tourists and a police officer, so hard to tell if it’s an anti-foreigner sentiment, but it is in the middle of this whole thing.”