The pair star as Simon Basset and Daphne Bridgerton in the Netflix period drama, which has been a massive hit worldwide since its release. Their intimate relationship on screen has led to speculation they might be an item in real life, but Page was quick to shoot down the rumours during an interview with Access Hollywood.
"I think that everything you need to know is on camera," he laughed. "The sparky words, scripts and material are more than enough."
Page's admission about his relationship with Phoebe came after he also opened up about reports he's in the running to take over from Daniel Craig as the next James Bond, after bookmakers' odds were slashed for him to take on the part.
"I think there might be an element of cultural translation to be done here," he said. "Like if you're a Brit, and you do something of any kind of renown, that people regard well, then people start saying the 'B' word (Bond). It's like a merit badge, you get the 'B' word merit badge."
"But I don't think it's much more than that. I'm very, very glad to have the badge. I'm glad to be in such wonderful company of people who have the badge. But it's a badge."
The new TV series is produced by Shonda Rhimes. It's one of her projects for Netflix following her departure from ABC after working for the Alphabet for 15 years.