The court is expected to be told that worldwide coverage naming the married man and his celebrity spouse has made an earlier injunction obsolete. A US tabloid magazine is among the publications named in complaints lodged by the internet privacy firm Web Sheriff.
It has asked Google to remove search links to articles in newspapers, magazines, blogs and websites including Facebook and Mumsnet.
It comes after the star was granted the gag to stop publication of his 'extramarital sexual activities' on the grounds of privacy. However, it has been ignored by newspapers and magazines around the world - including Scotland - and flouted by websites and Twitter users, prompting criticism that it was making an 'ass out of the law'.