The 36-year-old actress was apparently enjoying a meal with her new squeeze at an Italian restaurant in London's West End when things got a bit heated as fellow diners, including Gwyneth Paltrow, looked on.
'Kate was snogging Ned's face off, although he didn't seem to mind,' a source told The Sun.
'They were so into one another. Kate was almost straddling Ned at one point during the meal.
'They didn't seem to care who saw them, even though Gwyneth and pals were on another table and she didn't look too impressed.'
The couple are believed to have hooked up while they were both staying at Ned's uncle, Richard Branson's house in the Caribbean, which caught fire after being struck by lightning.