Price and the rugby player turned up at a Soho bar at 1am and didn't leave until 11am, according to The Mirror.
The pair had been working together on a photoshoot before heading to Balans bar and restaurant.
A photographer from the shoot wrote online: "Just finished the Jordan/Gavin Henson job. That was insane. Fair to say - he pulled!"
An onlooker at the bar said: "They arrived at 1am and immediately ordered a round of cocktails. It became apparent that there was a budding romance happening."
The source continued: "They both looked like they fancied one another and were not attempting to make any secret of it in front of other diners.
"Their date went on for hours. They were downing shots and getting very drunk indeed.
"At one point Katie was shouting very loudly. They were just drinking for hours and hours."
Henson and Price were pictured leaving the venue holding hands.
Henson is the first man Price has been linked to since splitting from boyfriend Leandro Penna in October.