The publicist said that there was no justification for French Closer to print the images and, like St James's Palace, drew comparisons with the media hounding of Prince William's late mother Princess Diana.
"I hope that the Palace sues the photographer and the magazine," Clifford said.
"It is clearly an invasion of privacy. I'm surprised, particularly considering what happened in France to William's mother 15 years ago."
He continued: "The good thing is no editor in this country has published them.
"If Kate was doing something dangerous or something that would upset the British public, then you could justify it. But her sitting by a private pool topless doesn't come into that."
Clifford added: "If the publisher knows that publishing a picture of Harry, William or Kate in a private setting will cost them a lot of money then they won't do it.
"If they pursue the French magazine and the photographer and successfully sue them - and it costs a lot of money - it's going to put everybody else off and that is why I hope it will happen."
Duchess of Cambridge at the Buckingham Palace garden party - photo gallery: