The pair were seen walking hand-in-hand and kissing following Monday night's Q Awards. The event saw Turner's act named Best Band In The World Today.
Turner was supposed to meet his bandmates at sushi chain Nobu, according to London Lite, but instead hooked up with Chung.
A source told the paper: “They walked into the bar together holding hands, and didn't seem to care who saw them together.
"No sooner had they bought a round of vodkas, they were snogging in the dancefloor - right in the middle of the club. She seemed totally smitten by him, and was laughing at his jokes and stroking his hair."
Chung used to present Popworld. Her friends previously denied rumours that she was seeing Turner earlier in the summer.