Eight officers from Plymouth Police E section emergency response team were pictured in The Sun on Plymouth Hoe with a headline: Thin Brew Line.
"Policing is full of wonderful real people... and all need to eat and drink!," Chief Constable Olivia Pinkney of Hampshire Police tweeted.
Devon and Cornwall Police were unavailable for immediate comment.
The paper pointed out the officers had stopped for 45 minutes at The Coffee Shack, which under police regulations they are allowed to do during an eight-hour shift.
But officers took exception to the "anti-police" coverage with Chief Constable Simon Edens of Northamptonshire Police, tweeting: "I encourage all officers & staff in @NorthantsPolice to take their break when they can, in or outside their station. #takeabreak #wellbeing."
Chief Constable Andy Cooke of Merseyside Police tweeted: "Shock horror. Police officers taking a break and drinking tea. In public! Brilliant scoop. Makes you proud of the British press."
Plymouth Police E section emergency response team tweeted: "We have been inundated with messages of support. As a thankyou the brews are on us if you are ever in our part of the world. #brewsforblues."
Photographer Wayne Perry told BBC News that when he took the shots he thought they would be used as a weather round-up.
"I was as upset about the way it was used as anyone and it was unfair but the officers did not help themselves," he said.
A Coffee Shack spokesman said: "If anything it was good PR for the police - at least you can go up and talk to them, which you can't if they're passing in a patrol car."
No-one was available for immediate comment from The Sun.
Senior police officers have defended a group of officers at the centre of controversy over a seaside tea break.