The Kills singer-guitarist has reportedly taken to calling the supermodel "Waynetta Slob" - the name of Kathy Burke's obese, chain-smoking character in 1990s sketch show Harry Enfield's Television Programme.
A source told The Sun: "Jamie likes to tease Kate. It's all done affectionately, but sometimes he pushes things too far.
"That was the case on their holiday when Kate didn't take kindly to her boyfriend's wind-ups."
They added: "Waynetta can never be bothered to do anything because she's 'smoking a fag'. That's something Jamie has become accustomed to with Kate."