Mr Justice Eady reportedly said in a hearing this afternoon that the publication of the player's name by the Sunday Herald and repeatedly on Twitter "made no difference" to the injunction.
This is the second time in a week that the Sun has gone to the high court in an attempt to have the gag lifted. The newspaper appeared in in front of Eady on 16 May alongside Imogen Thomas, the model with whom the player is alleged to have had an affair, but failed to have the gagging order lifted.
The player – known in the courts only as "CTB" – has been repeatedly named on Twitter since allegedly launching legal proceedings against the US-based social networking site and several of its users.
The action against Twitter related to an account that purported to name several celebrities that it alleged to have taken out injunctions.
Yesterday the Sunday Herald devoted its front page to a picture of the player with a thin black strip across his eyes.
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